SOLUTION: the sum of the ages of ryan and linda is 113. 9 years ago, ryans age was 4 times lindas age. how old is ryan now?

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Question 1108720: the sum of the ages of ryan and linda is 113. 9 years ago, ryans age was 4 times lindas age. how old is ryan now?
Found 4 solutions by Boreal, TeachMath, ikleyn, greenestamps:
Answer by Boreal(15235)   (Show Source):
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Linda=x
Ryan=y
x+y=113.9
9 years ago Linda was x-9
Ryan's was 4(x-9)=4x-36
Now Ryan is 4x-27, because it is 9 years later, so y=4x-27 and we can substitute
x+4x-27=113.9
5x=140.9
x=28.18 Linda
y=113.9-28.18=85.72 Ryan ANSWER
nine years ago, Ryan was 76.72 and Linda was 19.18, so Ryan was 4 times older than she.

Answer by TeachMath(96)   (Show Source):
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Ryan is 85. No other answer is correct.

Answer by ikleyn(52832)   (Show Source):
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.

R + L = 113, (1) R-9 = 4*(L-9). (2) ("9 years ago . . . ") =============> (113-L) - 9 = 4L - 36 113 - 9 + 36 = 4L + L ====> 5L = 140 ====> L = = 28. Answer. Ryan is 113 - 28 = 85 years old. <<<---=== EDITED

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There is a bunch of lessons on age word problems
    - Age problems and their solutions
    - A fresh formulation of a traditional age problem
    - Really intricate age word problem
    - Selected age word problems from the archive
    - Age problems for mental solution
in this site.

Read them and become an expert in solving age problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Age word problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
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to your archive and use it when it is needed.

Answer by greenestamps(13203)   (Show Source):
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Tutor boreal misread the problem and came up with a nonsensical answer.

Tutor teachmath showed the right answer but without showing any work, so it is of little use.

Tutor ikleyn, as usual, provides a good solution method, but in the end she gives Linda's age instead of Ryan's.

I would approach the problem a bit differently, like this:

If their combined ages is now 113, then 9 years ago it was 113-18 = 95.
At that time, Ryan was 4 times as old as Linda. So

9 years ago, Linda was 19 and Ryan was 4*19 = 76; now Linda is 28 and Ryan is 85.