SOLUTION: " The sum of Allan and Ben's age is 45. Seven years ago, Allan was 16 years more than one- half as old as Ben was then.

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Question 1012360: " The sum of Allan and Ben's age is 45. Seven years ago, Allan was 16 years more than one- half as old as Ben was then.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let: A = Allen's age NOW

Let: B = Ben's age NOW

Then: A-7 = Allen's age 7 years ago

And: B-7 = Ben's age 7 years ago.

Also: one-half as old as Ben was then = 1%2F2(B-7)

And: 16 years more than one- half as old as Ben was then =

1%2F2(B-7)+16

" The sum of Allan and Ben's age is 45.
A + B = 45

Seven years ago, Allan was 16 years more than one- half as old as Ben was then.
A-7 = 1%2F2(B-7)+16

So the system of equations is

system%28A%2BB=45%2CA-7=expr%281%2F2%29%28B-7%29%2B16%29

Simplify the second equation, first by multiplying
both sides by 2:

red%282%29%2A%28A-7%29=red%282%29%2Aexpr%281%2F2%29%28B-7%29%2Bred%282%29%2A16

2A-14=1%28B-7%29%2B32

2A-14=B-7%2B32

2A-14=B%2B25
2A-B=39

Now solve the system of equations:

system%28A%2BB=45%2C2A-B=39%29

Edwin