SOLUTION: Faith is 10 years older than Grace. Eight years ago, Faith was 3 times Grace's age. How old are they now?

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Question 1164417: Faith is 10 years older than Grace. Eight years ago, Faith was 3 times Grace's age. How old are they now?
Found 3 solutions by AndrewWillie, ikleyn, greenestamps:
Answer by AndrewWillie(2)   (Show Source):
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I think Fainth 32 and Grace 22

Answer by ikleyn(52814)   (Show Source):
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.
Faith is 10 years older than Grace. Eight years ago, Faith was 3 times Grace's age. How old are they now?
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Let x be the Grace age; Then Faith is (x+10) years old. Eight years ago they were (x-8) (Grace) and ((x+10)-8) = (x+2) (Faight) years old. The condition says x+2 = 3*(x-8). From this equation x+2 = 3x - 24 2 + 24 = 3x - x 26 = 2x x = 26/2 = 13. ANSWER. Grace is 13 years old; Faith is 13+10 = 23 years old. CHECK. 8 years age they were 13-8 = 5 and 23-8 = 15 years old with the ratio = 3. ! Correct !

Solved.

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    - Age problems and their solutions
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Answer by greenestamps(13203)   (Show Source):
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The difference in their ages is 10 years; 8 years ago, Faith's age was 3 times Grace's age.

Let x be Grace's age 8 years ago; then Faith's age 8 years ago was 3x. The difference in their ages then was 3x-x = 2x.

But the difference in their ages then was 10 years. So 2x=10, and x=5.

That means their ages 8 years ago were x=5 and 3x=15.

And that means their current ages are 13 and 23.