Answer:
Explanation:
You can use your number sense to reason your way through this problem, or you can write equations for it. If the father is 38 years older than his son, and that makes him twice as old, the son must be 38 and the father 76. This was the condition 10 years ago, so their ages now are ...
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If you prefer to solve a set of equations, you can assign variables f, s, to the father's age and the son's age respectively.
f = s +38 . . . . . . the father is 38 years older than the son.
(f -10) = 2(s -10) . . . . 10 years ago, the father was twice as old as the son
The first equation gives an expression we can use to substitute into the second equation:
s +38 -10 = 2s -20 . . . . substitute for f, eliminate parentheses
48 = s . . . . . . . . . . . add 20-s, collect terms
f = 48 +38 = 86
The father is 86; the son is 48.
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Additional comment
An age difference remains the same through the years. It is the same now as 10 years ago or 10 years in the future. A multiplying factor for ages gets smaller as years go by. Someone 3 times as old now will only be 2 times as old at some point in the future, for example.
The difference in ages is a multiple of the younger age that is 1 less than their ratio. In other words, if A is 3 times as old as B, the difference (A-B) is exactly (3 -1)×B = 2B. In the above problem, this was (f-s)=38; f/s=2, so we know 38 = (2 -1)s = s.