Question

Mark is 6 years younger than 2 times his brother. If their combined age is 24, how old is mark?

Answer 1

14

Explanation:

You want to know how old Mark is if he is 6 years younger than twice his brother's age, and their combined age is 24.

Relations

Let m and b represent Mark's age and his brother's age, respectively.

The given relations are ...

• m = 2b -6
• m + b = 24

Solution

Solving the second equation for b, we have ...

b = 24 -m

Using that in the first equation gives ...

m = 2(24 -m) -6

m = 48 -2m -6

3m = 42 . . . . . . . . . add 2m, combine like terms

m = 14

Mark is 14 years old.

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Check

Mark's brother is 24 -14 = 10. Twice that less 6 is 2×10 -6 = 14, which is Mark's age, as it should be.

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