At present: A = 3 * B In four years: A + 4 = 2 * (B + 4) Substituting for A in the second equation we get: (3 * B) + 4 = 2 * (B + 4) Simplifying we can write: 3B + 4 = 2B + 8 Subtracting 4 from both sides we get: 3B = 2B + 4 Now, subtracting 2B from both sides we get: B = 4 And substituting the value of B into the first equation we get: A = 12 Cross-checking we plug the values of A and B into the "in four years" equation and get: 12 + 4 = 2 * (4 + 4) Simplifying, we get: 16 = 2 * 8 QED

Mr. KZfaq man, you’ve ignited my second go with math. I appreciate you; your contribution to society has not gone unseen.

😳 I'm 64 yrs old and trying to stay sharp. What a challenge 😬thank you for your wonderful videos. I watch them often.😊

Right now Ann is 12 and her brother is 4. That’s 3x older. In 4 years Ann will be 16 and her brother will be 8. That’s twice as old.

I am 78 years old. I don’t remember learning any of this in high school. It’s so interesting and I am learning a lot. Thank you.

I solved this instantly without messing about with algebra. I also did what I used to do in school: reinterpret the words to match what was actually intended.

I love all the problems I can do, that you provide, as mental math. Thanks!

I chose Ann's age variable as A and the brother's age variable as B. This helps by eliminating the X and Y translation to their names.

I would like to say how much I enjoy your videos. Your explanations are crystal clear. Together with your soothing reassuring voice you make the problem easy to follow. I am an English language teacher myself and have been living and working in Italy for many years. I was not good at maths when I was growing up in London, but strangely enough I always liked it. Probably due to my enthusiastic Indian maths teacher, Mr Sharma. I do not think that you are obsessive, but I believe that you have a passion for your subject. I am subscribed to your channel, and I give you a like every time. Please continue to make videos. I will recommend you to my Italian students. They will pick up some good English and I am sure you will help them to sort out any difficulties they are having with their maths. All the best and have a nice day.

I have to say although I understand what is being asked for in this problem, I have a MAJOR problem with it's grammar. If Ann if 3 times older than her brother who is 4, then she would be 16 because 4 + (3 x 4) = 16, because she is 3 times "OLDER", which means 3 times his current age plus his current age. The correct wording should be Ann is 3 times "AS OLD". As you can see in the second sentence in the word problem the grammar is correct since they are using "twice AS OLD".

Love the channel but a word problem depends on language. As written, it clearly states Ann will be twice as old. It does not say twice as old as her brother but twice as old (as she is now). I solved it the way it was written. I do love the channel, and the math teacher who creates it. There is an inherent logic in language that cannot be denied legitimately.

I liked that problem, I figured it out before you had time to set up the problem, thanks for sharing this problem with us.

I simply looked at this through LCM (lowest common multiple) - the number 4 is key to my thought process. She is 12, and he is 4. 12 is 3 times more than 4, and in 4 years, she will be 16, whilst he would be 8 (twice his age in 4y). I had this solved in 30s, before the video started. And, I was right. Multiple ways to get to the right answer!

Thank you for the vid. Some math instructors want to see every step or points will be taken off. This was very clear.

Great video! That said, it seems a bit counter-intuitive to start with Ann = 2* Brother, seeing as that's starting from the end, and also working towards finding out his age in the future, not "now" as is requested. Seems like this would better translate to the following: Ann = 3*Brother // now Ann + 4 = 2 * (Brother + 4) // in 4 years So, replacing Ann on the lefthand side of the 2nd equation using the 1st one, and expanding the multiplication on the right side, we get: 3*Brother + 4 = 2*Brother + 8 Which leads to: 3*Brother - 2*Brother = 8 - 4 And then: Brother = 4 And that's the answer for his age *now*. Of course, everyone has different ways to approach problems, but for me, I find this to better match how the problem is presented.

She is 3 and her brother is 1. Their birthdays are both on feb 29, and she will be 4 and her brother will be 2 in 4 years from now.

Thank you for your videos. It is great for learning. I hope you do videos forever I will definitely be supportive. Also I hope you do basic math as well. I love word problems they help you think.😊

better phrasing would be in 4 years she will be twice his age

Love the comments on the wording used. I got the answer in about 15 seconds in my head. (always been good at math). Funny about 3 times older is the same as 4 times the age and that she would be twice as old (as herself now???) With that said I got the gist of it and chose bro as age 4.

I feel like you take eons to explain everything. But I so very much wish that I had a teacher like you 40 years ago when I took algebra. Thanks for your work and for your videos.

I have five younger brothers, so I figured it out by using the math in my personal life, and came up with the correct answer, in spite of your lack of English skills.

You can do it a bit different in how to express the ages and then do the algebra. But it is essentially the same thing you did. I know some people, find this a bit easier to visualize. Ann is the right side of equation and brother is the left. Today: 3x=y In 4 years: 2(x+4) = y+4 2x+8 = y+4 I then substrates the future age from todays age (you can to todays age minus future age as well if you want) to get rid of ‘y’. 3x- (2x+8) = y - (y+4) So i then get x-8 = -4 X= 4

I am ok at math(s), but this channels makes me smile, re-teaching me math(s) so I can help my kids when the struggle with their home work. Big thanks from the other sid of the pond.

Wow, after taking algebra 3 years in high school 30 years ago and failing all 3 times, I'm terrified of algebra,, I'm back to school now at the age of 62 I enrolled in college and I'm working on earning my bachelors degree in game art, one of the classes I'm required to take is college math, and I'm terrified that I'll fail the algebra portion. I've been watching all your videos and really paying close attention to your process and finally for the first time, I understood the process of the algebraic solution for this question, I actually guessed the answer correctly by doing deductive reasoning and came up with 4, but as you started to create an equation out of it I started thinking like you and I was ahead of where you were going the whole time and I'm so happy that I can now solve this problem by algebra and maybe by the time I have to take my college math course I will have learned enough from you that I won't fail. My goal is to graduate with a 4.0 gap and I'm on my 6th course right now and have a 4.0 gpa. We take one class for 4 weeks then we start the next class so I have 27 months of classes until I reach my degree and I will be thrilled if I can get an A in college math, I already aced psychology and college English composition and I have received 2 directors award submissions for having the highest grade in my art1 class as well as my technology and communications in the media industry course. So I'm on the right path, right now I'm studying 3D foundations and having to learn how to use different 3D animating and sculpting software programs and it is all based on geometry which because I couldn't pass algebra I never got to in high school. So I'm having to learn not only geometry and new software I'm also having to learn how to use a windows of from a Mac which I just started using the Mac in my first course 5 months ago after only using an I pad for 10 years and its been 15 years since I used a pic. I am taking a crash course on LinkedIn on how to use windows 10 and 11 and have been learning everything to do with a computer for 2 days now. I'm really excited to learn how to use a pic because when I was originally in college in 1982 I was asked if I wanted to take a course in the new computer lab and I looked in the room at those old bulky monitors with there little screens and green letters and I said no thank you, I think computers are just a fad like everything else in the 80’s and would never take off just like 8 track players. Boy was I wrong and as an artist it has been a battle between me and computers for 40 years, for the most part I could always beat computers and draw faster and more accurately than a computer could but as of the last 10 years computers have been catching up and beating me, and so I decided that if I wanted to survive as an artist I was going to have to embrace the computer and learn how to use them. Now with AI taking off at such a rapid pace I may become outdated before I finish my degree program as AI is advancing beyond the technology of the software I'm currently being trained on, so I'm learning how to embrace AI. And I know if I want to survive in the future I'm going to have to adapt to using AI. Technology as part of my artistic process because if I don't use it, I will just get left behind from the younger people that are using it. So at the age of 62 I'm staying up to date with technology and looking forward to opening my own home studio where I can work as a freelance remote working artist for the game in G art and design business. That's my goal for my golden years. I'm already retired but I'm looking for a late life career and not retiring permanently until I'm 90. I think I still can put another 30 years into a career .

Let Y be Ann’s current age, and X be her brother’s age. The first statement gives us: Y = 3X The next statement tells us in 4 years: Y + 4 = 2(X+4) If we substitute 3X in place of Y, we get: 3X + 4 = 2(X+4) 3X + 4 = 2X + 8 X = 4

Ann's 12 now & her brother's 4. In 4 years she'll be 16 & he'll be 8. Easy again.

This is why i love math! I had the right idea, just made one goof, which is all it takes. It really jiggled my memory cells. I love this. I have a problem for you i have not been able to solve. How do i send it to you? When we go to the big city, i have 5 hours driving which gives too much time to think of things and pit stops. So, i ask questions about my encounters and time etc... When i mention the math questions to others, they think i am nuts. No, just very curious, and they aren't. The hav e their fun, i have mine. After i took Algebra, i even saw it in a dance the kids were doing at a Spanish Club dance. There was no oneto talk to about it. I wanted to write it down, but no way to do it, and later, i could not remember the pattern. I asked my math prof who had figured these things out (history), and what is the practical application ? She said those were questions for greater minds than hers. I thought it a rather sad answer. Later i dated a guy who installed wood stoves. He used it to figure out the pitch of the roof so he could order the correct parts. I imagine he may have needed it for other installment issues, too, but that is what learners need in order to comprehend how and why it works. Maybe they do that now. '93 was my last class. Thank you.

What these type of relative age problems deal with are differences in age multiples of the older person between a specified number of years. The general formula can be described as (ax - bx) = d. 'x' represents the age of the brother which is what we are trying to solve. 'a' is the current multiple of her brother's age (how many times older she is currently) and 'b' the future multiple of his age. 'd' represents the difference in years (ie: how much time will have passed) between the the first and second multiples. You could also write this in its factored form: [ (a - b) * x ] = d as long as one doesn't mind an extra set of brackets! This is easier to simplify down to: x = d / (a - b) This generalized equation would also work for the less neater variety of inputted data, including non-integer multiples of age. If the problem were described as Anne being 7.5 times older than her brother currently and in 9 years she will be 4.25 times older then the equation of: 7.5x - 4.25x = 9 would simplify to: 3.25x = 9 yielding: x = 2.77 (rounded to two decimal places). The decimal portion would just be an expression of a part year, approximately three quarters. Thus Anne's brother for this scenario would be just a fraction over 2 3/4 years old currently.

THANKS!WE WERE ABLE TO UNDERSTAND CLEARLY!!.daniel & miss cirila.CANADA.

I got by trying different numbers. I like this guys voice.

Being an old person and not knowing algebra, I did it the grade school way: 1x3=3, +4=7 (not divisible by 2) 2x3=6, +4=10 (2+4=6 and 10/2 is not 6) 3x3=9, +4=13 (not divisible by 2) 4x3=12, +4=16 (4+4=8, 16/2=8) And I agree with other posters... the grammar left this question possibly confusing...

Loving this ❤

You don't need to subtract 2X from both sides. Move the positive 2X from one side of the equation to the other it becomes negative. Any time a term crosses the equal sign it changes to the opposite; positive becomes negative, multiplication becomes division... This is the way I was initially shown to do it when I was a junior in high school, and it is the correct way. It involves fewer steps and makes you think about what is happening. I was shown the right way first but later, the instructors tried to poison my mind with the incorrect way that involved unessecry steps.

Thank you for this video

Another good example of using the Gaussian elimination or matrices techniques.

I REMEMBER that now! THANKS!!

Wonderful teacher. I had these skills once upon a time because my high school teacher was brilliant but that was 55 years ago. Thank you for bringing this back.

Fascinating

This isn't too bad; (i) 3b = a and (ii) a + 4 = 2(b + 4). Solve, giving b = 4. a being annes age and b being her brothers age.

I did it in a slightly different way. I said: Ann = X and Brother = Y. Then X must be 3Y (because Ann = X = 3 times older than Brother = Y). So I did the following: X = 3Y so 3Y + 4 = 2 (Y + 4) => 3Y + 4 = 2Y + 8 => Y + 4 = 8 => Y (Brother) = 8 - 4 = 4. Ann = 3Y = 3 x 4 =12 (and 3 x 4 = 12). Four years later Y (Brother) = 4 + 4 = 8 and Ann = 3Y + 4 = 3 x 4 + 4 = 16 (and so Ann is two times older than her brother after 4 years (2 x 8 = 16).

Shouldn't the first sentence be constructed "Ann is 3 times as old as her brother?"

I feel like we need a reading comprehension lesson rather than a math lesson. This is a very easy problem to solve actually. You will get two "correct" answers, depending on how you interpret the "In four years she will be twice as old".

I don't normally post in your comments, but I have to say this... Your word puzzles are written concisely! Keep up the good works! Here brother is 4 years old. He will be eight, and she will be sixteen in four more years! Love you mathematical puzzles!

This is fun!

Im 75 and i love these problems. I nver got them wrong back then in school !

2 things: First, I like to use variables that reflect the problem. I.e., let A = Ann's age, and B = Brother's age. Second, translate each sentence into an equation: Ann's age is 3 times Brother's age--> A = 3 x B.

Will she be twice as old as she currently is or twice as old as he is in 4 years? Assuming the latter, A=3B and A+4=2(B+4), so 3B+4=2B+8 and Ann’s brother is currently 4.

Wow! This word problem was real tricky like a riddle being told to me. But the requested answer being ask for the brother was a lot simpler than I had thought. The answer is, the brother is now 4 years old. An additional thought: I'm curious to know about the sister's present age as well If the sister is twice as old as her brother, does this make her age 8 years old or 12 years old in the present time since she is still 3 times older than her little brother?? I'm thinking more towards that the sister is no longer 3 times older, but is (now) twice as old as her little brother in present time. So...now, sister is 8 years old? Am I wrong?

Thanks

Do you know when I ran into problems like this at school I found them almost insolvable truly impenetrable, and hey guess what, I still don't understand; unlike most posts here. There are obviously there must be rules that I didn't get taught or was expected to intrinsically know. I will watch it again

I solved the equation by multiplying 3x4=12 for ann”s years and divided 3/12 =4 for her bothers year. if we add 4 he would be eight and she would be 16. the same scenario would have of it were 3x5 years older 15 means he is 5 + 5 years she is 20 and he is 10. or 3x 6 years she would be 18 and he would be 6 in 6 years they would be 24 and 12. I really dont remember how to do linear algebra. the same for 7x3=21 + 7 is 28 /2=14. But I will practice the hard algebra way so I can remember. I remember in the 80’s in grade school doing the CAT’s . I got a perfect score of 12.9 going into high school, but I did not understand algebra’s formulas. Somehow I had my own fomula’s with regular math and blocking in my head to get the answers really fast. I am a pre-senior today a d I want to know all of the formulas and become a mathematical genius before I turn 60. How old am I today? 😂😂😂

I love your videos - genuinely I do. But you need to more carefully phrase the second statement. It says “In 4 years she will be twice as old”. It does not say “twice as old as her brother”. One can say it is implied, but then that could have been flipped around to say “Ha, I didn’t say twice as old as her brother.” Probably won’t agree, but I still love your videos.

After pausing the video I of course overcomplicated this thing as a pair of equations: a = Ann's current age b = Brother's current age Initial Equations: a = 3b

❤❤❤❤❤I LOVE IT SO MUCH AND KEEP IT UP

I solved it before watching the video. Had to go back about 50+ years to remember how to do this. HOWEVER, this demonstrates my problem with how we teach math. No one will ever use algebra to get this answer. They will just ask Ann’s mom how old her brother is. So to effectively teach math we need real world problems, not made up riddles. I recall learning binary math. Remember how old I am (you can approximate my age based on the information I have supplied). I asked my teacher, “Why would anyone use a math system with only 2 number? Especially when they have 10 fingers?” Her answer was, “It’s in the book and we have to learn it.” It wasn’t until 10 years later (more help estimating my age) when I got a real job working on computer terminals that I realized the practical value of the binary system. To this day computers function on based on 0s and 1s. Would have been helpful to me to know that in class. I would have seen a purpose for the math. I was not one of those students who was challenged by the problem itself. If it didn’t have practical value, learning it was pointless to me. So the big question that I still don’t know the answer to - what is the practical application of this problem? Real world useful example?? Serious question, but I appreciate the challenge to remember what I learned in the last century. Good video.

I actually did guess and test and got it on the first try. When thinking algebraic I used two variables and two equations.

Never went to high school no algebra got a machine shop job 1966 OMG Did it till 2020 School of Hard Knocks ( you sure make it easy to understand ) Thanks so much 🙏 I'm to old to use any of it

No wonder I was never good at word problems

I thought it would be easy. Then I got confused. Now i get it. thanks.

I came up with the answer "4", but I don't know how. I just figgered it out.

4. Did it in my head in 15 secs.

I solved it correctly! I had a Mohawk in 1983. I have a Mohawk this morning in 2023. The Mohawk makes ALL the difference in my maths skills.

I see two solutions for the problem statement. The one you have performed here assumes that she was to be twice as old as her brother in 4 years. I read it as Ann being twice as old herself. The problem statement is not clear so the solution must have two possible solutions. Can you write a possible formula for the second solution?

Presently Ann is 12 and her brother is 4. Ann is 3 times older. Fast forward 4 years, Ann is 16 and her brother is 8. Ann is now twice his age.

The key to every solution is the proof that it worked. One missing link could be filled in here by testing the result and filling out the table to check your work.

Don't hate me, but I wrote an equation after reading just the first sentence. I wrote down "a = 3b". Then I read the second sentence and wrote "a+4 = 2(b+4)". Then, and only then did I read what they were asking for. After that I just substituted 3b for a in the second equation and solved it the same way you did at that point.

4 Somehow I'm able to look at math problems and intuitively know the answers. I don't know how I'm able to do this but it's something I've always been able to do. However that isn't actually the solution to the question. The real solution is the procedure and equation that allows you to solve it and that's something I've always had trouble with. In school despite having the correct answers I often got the problems wrong because how I solved them wasn't correct. Everyone always said "he's really good at math" but I consistently had a C average. lol

@tabletclass Your answer is wrong! Based on the word problem it states she is currently 3 times as old as her brother then states in 4 years she will be twice as old. Which means she’s 4 years old if in 4 years she’s twice as old as she is currently. This will make her brother currently 16 months old. The problem does not state in 4 years she’ll be twice as old as her brother but only that she’ll be twice as old. You never assume in math! Remember assume is spelled ass-u-me

Did this one in my head without algebra butstill fun.

At 15:55 you should subtract 4 on both sides, you are missing the minus sign on the right side of the equation. Greetings from Switzerland

I thought it was a trick question at first because of the second sentence, “In four year Ann will be twice as old” instead of, “…. Ann will be twice as old As Her Brother”.

If you say Ann's age is 3x. The wording to this would be: Ann is 3times as old as her brother

Hello everyone, here is my solution, without watching the video or reading the other comments: x = current age of Ann y = current age of Ann’s brother (a) x = 3y (b) x + 4 = 2 ‧ (y + 4) Subst. (a) in (b) 3y + 4 = 2 ‧ (y + 4) 3y + 4 = 2y + 8 | -4 3y = 2y + 4 | -2y y = 4 | Subst. (a) x = 12 CONTROL (a) 12 = 3 ‧ 4 12 = 12 (b) 12 + 4 = 2 ‧ (4 + 4) 16 = 2 ‧ 8 16 = 16 qed Best regards Marcus 😎

I hated story problems when I was in school! Sure wish you had been around then. Maybe I wouldn't fear math so much.

I enter my 8th decade in London next year and did it in 7 seconds(approximately),genuinely.

15 seconds solved in A.I. head and 10 minutes to construct problem, differently mind you. 3X+4/2=2X, ....... 3X+4=4x......or 4X=3X+4......4X-3X=4.....X=4 Brother=4 years old

16:12 / 18:38 Ann is 3 times older than her brother means she is 4 times as old so, if you mean she is 3 times as old, say that. the answer is 6. when the brother was 2 ann was 8 (4X) 4 years later she is 2X6, or 8+4 or 12.

Ann is 12 Brother is 4 system of equations a=3b a+4=2(b+4) use substitution.

Withh the giveninformation,you get 2 independent equations.Let the age of Annbe a and the age of hher brotherb, then you get: a=3*b a+4=2*(b+4) If you substitute a withh 3*bin thhe second equation, you get: 3*b+4=2*(b+4) 3*b+4=2*b+8 b=4 With this result, you get from the first equation: a=3*b=3*4=12 So Ann is 12 years old and her brother is 4 years old. in 4 years, she will be 16 yeas old and her brother will be 8 years old.

Its obviously recommended to do it the algebraic way, but you can actually get to the answer pretty quickly via guess & check. For starters: We know that the brother must be an even number of years old. If he was odd, the math becomes impossible. To prove that: Suppose the brother is an odd number of years. If Ann is three times older, that means she is also an odd number of years old. Because multiplying three [odd] by any other odd number will always return an odd value. So if the brother is odd, Ann must be odd. But here comes the issue: In 4 years, Ann needs to be TWICE the age of her brother. an odd number plus an even number will always result in an odd number. So if Ann is 7, in 4 years she'll be 11. 11 does not divide into 2. Not does any other odd number. Therefore, her brother cannot be an odd number of years old currently. From there, let's proceed to guess & check. You're welcome to try a larger number for her brother's age, like 20. That would put Ann at 60. In 4 years, they'll be 24 & 64. That's not particularly close to being twice as old. Still much closer to three times as old, really. The larger you go in the brother's initial age, the worse this problem becomes (and sadly, the less likely it is for Ann to still be alive.) So its easier to just start from 0. That will fail. 2 will fail. Hey, 4 works. Obviously this is a long way to get to the same answer. And arguably even requires a mind that is already familiar with math, to the point where doing it the right way is simpler for that person anyway. But this was actually how I went about it since I didn't have pencil and paper to write everything else down in front of me, haha

The answer is 1 year and 4 months. For her to be twice as old she has to be 8. Divide 4 years by 3. That's the way it reads.

At Four minutes of the Clip, thats when He starts to Teach, then loses His chain of thought, then comes back 😢. Still i subscribed and learned something, even tho He still loses his chain of thought.😊😊.

let Anne's age = a and her Brother's age = b then we simply have simultaneous equations a = 3b and a+4 = 2(b+4) which simplifies to a + 4 = 2b + 8 and then a = 2b+4 Subtracting the simplified second equation from the first gives 0 = b - 4, therefore b = 4. There's the answer. Putting back in to double check, a = 3b = 3(4) = 12. In four years Anne is 16 and her Brother is 8. All good.

The ages now are Ann 12 brother 4

My algebra skills were not working on this one to set up the formula correctly. So I try old and aired it. And I got it correct. My algebra came out too old.

In the end, everything comes down to basic math!! Doesn’t matter what the concept is!!

Ann is 12 now and her bro is 4. In 4 years Ann will be 16 and bro will be 8. A=3b. A+4=2(b+4) so 3b+4=2b+8 giving b-4=0 so b, her brothers initial age is 4. Ann is 3 times that so she initially 12. In 4 years she will be 12+4=16 and bro will be 4+4=8 which is half of 16.

12 & 4

I love word problems

My equation: 3(X)=2(X)+4...solving for X yields: 3X-2X=4; thus X=4yrs. old.

Seems too messy. How about doing 2 equations, 2 unknowns With variables of “a” for Ann age, “b” for bro’s age Equation 1 a = 3b (Ann is 3 times bros age, or 3 times bros age is Ann’s age) Equation 2 a + 4 = 2(b + 4) Which equals a = 2b + 8 - 4 Now reduce to just one equation with one unknown as 3b = 2b + 4 3b - 2b = 2b - 2b + 4 b = 4 (bros age) Using 1st equation a = 3 * 4 a = 12 ( Ann’s age)

I think that the wording should be …Anne is three times AS OLD as her brother ( and not three times older than her brother ).Three times older means that she is presently four times her brother’s present age.

???? Got it on first try on my own. Still remember in my 70s. Question: can non -students get your courses?

I despise word problems, but I will force myself to hang in there.😭

I did it a little bit different: Ann = x, Brother = y Today x = 3y, in 4 years x = 2y + 4 ==> 3y = 2y + 4, ==> 3y - 2y = 4, ==> y = 4 Her Brother is 4 years old today.

this one was easy to reason out without algebra. We already know the answer has to be an integer in the range of life span of humans. So, first try the simplest answer. Three time older could 1 and 3, 2 and 6, 3 and 9, etc. but it also can only be double in 4 years. Try 4 because 3 times 4 is 12 and adding 4 to both is 8 and 16. Easy peasy. But most real world problems are not this simple and usually don't have to be integers.

Three times older or three times as old?

Could it be argued that "three times older than" could be interpreted as "3x + x"? I think a more clear wording would be "three times the age of" if it is to clearly imply "3x" Since "100% = 1x, thus 300% = 3x" and "100% larger than = 1x + x, thus 300% larger than = 3x + x"

4 years old

Key point: Moving the variables to the left of the equation to have only numbers to the right. Got it! You only gave the rule without explaining the logic of it though. If one wants to understand what one is doing one needs explanations. ;) But why substracting 2x and not adding it both sides instead. :( Because we need to get rid of the variables on the right side of the equation. You kind of jumped the gun a bit at this crucial point of the solution. That's why some may want to do video games instead. Respectfully!