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A man is 42 years old and his son is 12 years old. In how many years will the age of the son be half the age of the man at that time? Explain!

After x years have passed, his father will be twice the age of the boy.

The age at this time of the father will be 42+x and the age of the son will be 12+x.

At that time, we know that the father is twice as old, so 42+x = 2(12+x)

Multiplying this out gives 42+x = 24+2x.

Adding -24-x to both sides gives 18 = x.

To check, let's see what happens 18 years from now. The dad will be 42 + 18 = 60 and

the son will be 12 + 18 = 30. Since 60 is twice 30, that's the right answer.

Algebra

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