Question: Ages of Ebo and Atu

Comment on Ages of Ebo and Atu

Hi Brent,
How could it be solved by assigning 1 variable? I could solve by test the answer though takes a lot of time but don't know how to approach by using 1 variable.
Thank you
gmat-admin's picture

Using 1 variable is a little trickier.
One approach is as follows:
Let A = Atu's age FIVE YEARS AGO
So 3A = Ebo's age FIVE YEARS AGO
Now let's determine their ages 3 years in the FUTURE (which is 8 years away from 5 years ago)
A + 8 = Atu's age IN THREE YEARS
3A + 8 = Ebo's age IN THREE YEARS
We're told that, in 3 years, Ebo is TWICE as old as Atu.
So, to make their futures ages EQUAL, we must double Atu's age. We get:
2(A + 8) = 3A + 8
Solve to get: A = 8
Since A represents Atu's age FIVE YEARS AGO, then Atu's PRESENT age is 13
Likewise, we see that 3A represents Ebo's age FIVE YEARS AGO. So, age FIVE YEARS AGE was 3(8), which equals 24.
So, Ebo's PRESENT age is 29
So, the sum of their PRESENT ages = 13 + 29 = 42

Hi, I did it using single variable as you have shown above.
However, I am still not clear what are the best way to solve the word problems:
1.) either using single variable or by using double variable ?
2.) Assuming current age as A+5 (and take 5 yrs ago as A) OR assuming present age as 'A' and 'A-5' five year ago.
Pls advice in which chase the equation will be simpler.

gmat-admin's picture

Good question. I cover those questions in the following videos:

How Many Variables to Assign:

Solving GMAT Age Questions:

Hi Brent,
I tried solving this way: Can you tell me what am I missing?

Atu age´s 5 years ago: A-5
Ebo age´s 5 years ago:3(A-5)
Why it doesnt´work?
gmat-admin's picture

Your equation A-5 = 3A-15 suggests that Atu age´s 5 years ago = 3 TIMES Atu age´s 5 years ago. This cannot be true.

It's like saying, the money in my bank account = 3 TIMES the money in my bank account.

To solve this question, you need to use the second piece of information (In 3 years, Ebo will be twice as old as Atu)

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