SOLUTION: A mother is five times as old as her son. If twice the age of the son is 3 years less than half of the mother, how old are they?

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Question 233484: A mother is five times as old as her son. If twice the age of the son is 3 years less than half of the mother, how old are they?
Answer by Theo(13342) (Show Source):
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let m = the mother's age.
let s = the son's age.

m = 5*s

Twice the age of the son is 3 years less than half of the mother's age.

2*s = (1/2)*m - 3

replace m from the first equation with 5*s in the second equation to get:

2*s = (1/2)*5*s - 3

multiply both sides of the equation by 2 to get:

4*s = 5*s - 6

subtract 4*s from both sides of the equation and add 6 to both sides of the equation to get:

s = 6

since m = 5*s, this makes m = 30

2 * 6 = 12

30/2 = 15 - 3 = 12

12 is twice the age of the son.
12 is half the mother's age minus 3

since they're the same, looks like we're good.

mother is 30 years old.
son is 6 years old.