Quandaries and Queries


Name: Jennifer
Who is asking: Parent
Level of the question: Secondary

Question: Mario is 16 years older than his youngest sister, Mercedes. Together, their ages total 36 years . How old is each person?

My daughter has been struggling with problems like this and I don't remember how to work them to help.



Hi Jennifer,

I want to show you two ways to solve this problem. The first is the method I prefer, it is really just using some number sense. Some people call this method "guess and check".

If Mario and Mercedes were the same age and the sum of their ages were 36, then they would each be 18 years old. But they are not the same age, Mario is 16 years older, so if Mercedes were 8 years younger than 18 and Mario were 8 years older than 18 then the sum would still be 36 but the difference would be 16.

Now the check.

Mario's age: 18 + 8 = 26
Mercedes' age: 18 - 8 = 10
Difference in the ages: 26 - 10 = 16
Sum of the ages: 26 + 10 = 36

If this seems like to big a jump you might do it in steps. If they were both 18 the sum is 36 but the difference is 0. If Mario is one year older then Mercedes has to be one year younger to keep the sum at 36, and now the difference in their ages is 2. If Mario were 2 years older than 18 then again Mercedes would need to be 2 years younger to maintain a sum of 36, and now the difference is 4 years. Keep going until the difference is 16.

The second method is to use algebra.

Let M be Mario's age and S be his sister's age. Then I know two facts

M is 16 years larger than S: M = S + 16
The sum of M and S is 36: M + S = 36

Thus you have

M = S + 16
M + S = 36

In the second equation replace the letter M by S + 18 (which you know from the first equation). Thus the second equation becomes

S + 16 + S = 36


2S + 18 = 36
2S = 36 - 16 = 20

and hence S = 10.

Now from the first equation M = S + 16 so M = 26.