SOLUTION: The sum of the ages of Mary and Elisha in four years is 49. Six years ago, Mary was 9 years older than Elisha. How old are they now?

Question 1190917: The sum of the ages of Mary and Elisha in four years is 49. Six years ago, Mary was 9 years older than Elisha. How old are they now?

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!

Simple, ready for Elimination Method.

Subtracting: e=16
Adding: m=25
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Translating the given information directly into equations in two variables makes for more complicated equations to set up the problem and more complicated algebra to solve it. If you are going to use formal algebra, digest the problem before plunging into an algebraic solution to find an easier way to set the problem up.

If Mary was 9 years older than Elisha 6 years ago, then the difference between their ages is always 9 years. So
x = Elisha's age
x+9 = Mary's age

4 years from now the sum of their ages will be 49.

You could say that their ages 4 years from now will be x+4 and x+13 and solve the equation that says the sum of their ages will be 49 then. But I think it is easier to say that, since the sum of their ages in 4 years will be 49, the sum of their ages now is 41 (49 minus 4 for each of them).

Then the equation is far simpler:

x+x+9=41
2x+9=41
2x=32
x=16

ANSWER: Their ages are x=16 and x+9=25.

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