Sam is 4 years younger than Amy. Five years ago, he was half her age. How old are they now?

Solution:

Consider x as Sam’s age and y as Amy’s age

Express the given statements as linear equations.

x = y - 4 ------->(1)

Five years ago

x - 5 = (y - 5)/2 ------>(2)

Let's solve this system of linear equations.

Substituting the value of x

y - 4 - 5 = (y - 5)/2

y - 9 = (y - 5)/2

2y - 18 = y - 5

By further simplification

2y - y = -5 + 18

y = 13

Substituting the value of y

x = y - 4

x = 13 - 4

x = 9

Therefore, Sam’s age is 9 and Amy’s age is 13.

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Sam is 4 years younger than Amy. Five years ago, he was half her age. How old are they now?

Summary:

Sam is 4 years younger than Amy. Five years ago, he was half her age. Sam is 9 years old and Amy is 13 years old.