SOLUTION: Annilee's present age is two-thirds of Jessie's present age. In 12 years the sum of their ages will be 54 years. find their ages.

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Question 328628: Annilee's present age is two-thirds of Jessie's present age. In 12 years the sum of their ages will be 54 years. find their ages.
Answer by Earlsdon(6294) About Me  (Show Source):
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Let A = Annilee's present age and J = Jessie's present age.
A+=+%282%2F3%29J "Annilee's present age is two-thirds of Jessie's present age."
%28A%2B12%29%2B%28J%2B12%29+=+54 In 12 years the sum of their ages will be 54 years." Simplify this equation.
A%2BJ%2B24+=+54 Subtract 24 from both sides.
A%2BJ+=+30 Now substitute the A+=+%282%2F3%29J in the first equation for the A in this equation.
%282%2F3%29J%2BJ+=+30 Simplify and solve for J.
%285%2F3%29J+=+30 Multiply both sides by 3%2F5
J+=+18 and...
A+=+%282%2F3%29J
A+=+%282%2F3%29%2818%29
A+=+12
Annilee's present age is 12 and Jessie's present age is 18.