Question 1153882: Ben is six years younger than his sister. After 10 years the sum of their ages will be 50. What are their present ages? Found 3 solutions by josgarithmetic, greenestamps, ikleyn:Answer by josgarithmetic(39617) (Show Source):
A solution without formal algebra -- using logical reasoning and simple arithmetic instead....
If the sum of their ages 10 years from now will be 50, then the sum now is 30.
So the two ages are two whole numbers with a sum of 30 and a difference of 6.
One way to solve this kind of problem quickly is to reason that the two numbers 15 and 15 have a sum of 30 but are the same; to get a sum of 30 with a difference of 6 between the two numbers, add 3 to one of the 15s and subtract 3 from the other -- giving you the numbers 18 and 12.
Since the equation is written INCORRECTLY in the post by @josgarithmetic,
I came to bring a correct Algebra solution.
Let sister's age be x; then Ben's age is (x-6).
In 10 years, their ages are (x+10) and ((x-6)+10).
So, the equation for the total age in 10 years is
(x+10) + ((x-6)+10) = 50.
Simplify and solve
2x + 14 = 50
2x = 50 - 14 = 36.
x = 36/2 = 18.
ANSWER. The sister is 18 years old. Ben is 18-6 = 12 years old.
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