# How to Solve Problems by Working Backwards Part 2

In the previous post, we have learned how to solve number problems by working backward.  In this post, we discuss age problems. We already had 2 examples in the previous post in this series, so we start with the third example.

Example 3

Arvin is 5 years older than Michael.  The sum of their ages is 37.  What are their ages?

Solution

This is very similar to the problems in the previous post in this series.  Arvin is 5 years older than Michael, so if we subtract 5 from Arvin’s age, their ages will be equal.  But if we subtract 5 from Arvin’s age, we also have to subtract 5 from the sum of their ages. That is,

37 – 5 = 32.

Now, their ages are equal, so we can divide the sum by 2.  That is 32 ÷ 2 = 16.  This means that the younger person is 16 since we subtracted 5 from Arvin’s age. Therefore, Michael is 16 and Arvin is 16 + 5 = 21.

Check

16 + 21 = 37.

Example 4

Mia is 3 years older than Pia.  In 4 years, the sum of their ages is 35. What are their ages?

Solution

There are two of them and we added 4 to both ages, so subtracting 8 from 35 (the sum) will determine the sum of their present age.  That is 35 – 8 = 27 is the sum of their present age.

Next, Mia is 3 years older than Pia, so if we subtract 3 from the sum of their present age, their ages will be equal. So, 27 – 3 = 24.

We can now divide the sum of their ages by 2.  That is 24/2 = 12.

This means that 12 is the age of the younger person because we subtracted 3 from the age of the older person.

So, Pia is 12 and Mia is 15.

Check 12 + 15 = 22.

In the next post, we will discuss more problems that can be solved by working backward.

### 5 Responses

1. Henry says:

I think example #4 is wrong, the correct is Pia 16 and Mia is 19. So the sum of their ages will be 35.

• Arvin says:

Nope. #4 answer is right. “In 4years” the sum of their age is 35. To know their present age. Subtract 8.. 4yrs for pia and 4yrs for mia. That’s why we get 27.. then subtract 3.. bcoz pia is younger that mia. 24 is the remaining .. then divide by 2 to get the age of the younger which is pia. Then add the 3 to get mia’s age bcoz she is 3yrs older than pia.. 🙂 got the wrong answer first. Then I analyze. Hahaha that’s why many are not passing the exam.

2. imaw says:

I think on example 3…Arvin should be 21 and Michael should be 16

3. Arnold says:

Example #3 arvin is 5 yrs older but michael is 21yrs old while arvin is 16

4. Arvin says:

Arvin is 5yrs “older” than micheal.. then it should be Arvin is 21 and micheal is 16.