Question: Ages of Ebo and Atu

Comment on Ages of Ebo and Atu

Can you add how to do this with one variable? I've been trying and keep getting stumped!
greenlight-admin's picture

Sure thing.
Let A = Atu's age 5 YEARS AGO.
This means 3A = Ebo's age 5 YEARS AGO.

That was 5 YEARS AGO. To find their ages 3 YEARS FROM NOW, we must add 8 years to the above ages.
So, A + 8 = Atu's age 3 YEARS FROM NOW
And 3A + 8 = Ebo's age 3 YEARS FROM NOW

We're told that, 3 YEARS FROM NOW, Abo's age will be TWICE that of Atu's age
In other words, 3A + 8 = 2(A + 8)
Expand: 3A + 8 = 2A + 16
Solve to get: A = 8
This means that Atu was 8 years old 5 YEARS AGO.
And it means EBO was 24 years old 5 YEARS AGO.

So, their CURRENT AGES are: Atu - 13 years old and Ebo - 29 years old
The SUM of their CURRENT ages = 13 + 29 = 42

Is there a way to solve this with two variable substitution?

E = 3A + 10
E = 2A + 3
------using the 2nd equation------
E = 2A + 3
E - 3 = 2A
A = E/2 - 3/2 (Substitute this into the first equation)

I get E = 11
greenlight-admin's picture

Be careful. You made a mistake when took the equation 3A - E = 10 rewrote it as E = 3A + 10.

Take: 3A - E = 10
Add E to both sides: 3A = E + 10
Subtract 10 from both sides: 3A - 10 = E (you have E = 3A + 10)


I have trouble when I work with this kind of problems. In the table I included the relationship between one age to another one. Is my mistake.. Could you please share another link to work with similar problems. Thanks so much.
greenlight-admin's picture

There are some extra practice questions in the Reinforcement Activities box here:


sir could you share some pratice problems for age ques.
greenlight-admin's picture

Check out the linked practice questions in the Reinforcement Activities box here:

Hi Brent, can you please help in solving this question without variables and using the options?
greenlight-admin's picture

The details of this question are far too complicated to test the answer choices.
It's important to note that most Problem Solving questions can't be solved by testing the answer choices, but we should always be on the lookout for opportunities to test the answer choices, since that approach can often be much faster.

For this question, we are asked to find the SUM of their ages now.
So, for example, answer choice C tells us that the SUM is 28 years.
Since we only know the SUM of their ages, it's extremely difficult to use this information to test whether C is the correct answer.

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