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A man is 24 years older than his son. 12 years ago, he was five times as old as his son. What are the present ages of both?

A man is 24.

Call the father's current age x and the son's current age y.

He is 24 years older, so x = y + 24.

The part on 12 years ago says that x - 12 = 5(y - 12).

Putting in the equation for x gives y + 24 - 12 = 5(y-12).

Simplifying the left and multiplying out the right gives y + 12 = 5y - 60.

Adding -5y - 12 to both sides gives -4y = -72.

Dividing by -4 gives y = 18.

Since x = y + 24, and y = 18, this means x = 42.

Checking out the age 12 years ago means the father was 42-12 = 30

and the son was 18-12=6. Note that 30 = 5*6, so that's the correct answer.

Algebra

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