Ann is 3 times older than her brother. In 4 yrs, she will be twice as old. How old is her brother?

How to solve an algebra age word problem step by step.

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[sda]

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

[jessi]

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

[cfrankwolfe]

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.

[mikesirignano]

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.

[jarvisfamily]

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

[lizadams]

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.

[randys]

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.

[kellpt]

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.

[WhitentonMike]

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.

[iane]

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!

[alfredosolari]

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.

[lakewrites]

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.

[omavicmcmurray]

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

[RodDavisSaints]

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!

[KenCool]

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 is 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".

[Kleermaker]

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).

[Caulderone]

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

[richlee]

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.

[gtf]

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

[deltalima]

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.