SOLUTION: Mary is ten years younger than twice Susan's age. Five years from now, Mary will be eight years older than Susan's age at the time. How old are Mary and Susan?

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Question 113476: Mary is ten years younger than twice Susan's age. Five years from now, Mary will be eight years older than Susan's age at the time. How old are Mary and Susan?
Answer by solver91311(12126) About Me  (Show Source):
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Let's say Mary is m years old, and Susan is s years old. So twice Susan's age is 2s. Ten years younger than that is 2s - 10. Since that is Mary's age now, we can write:

m+=+2s+-+10

Five years from now, Mary will be m + 5 years old, and Susan will be s + 5 years old. And the problem tells us that Mary will be eight years older than Susan then. So we can also write:

m+%2B+5=s%2B5%2B8 or
m%2B5=s%2B13

Since we know that m=2s-10 we can substitute this expression in the second equation.

%282s-10%29%2B5=s%2B13

Now solve for s:
2s-5=s%2B13 Collect terms
2s-s=13%2B5 Add -s and +5 to both sides
s=18

So Susan is 18. Let's put this value back into the first equation.

m=2%2818%29-10
m=26

And Mary is 26.

Last step -- Very Important. Check your answer.

26 = 2 * 18 - 10, 26 = 26 Check and
26 + 5 = 18 + 13, 31 = 31 And both answers check.

Hope that helps,
John