SOLUTION: Susan has saved $85.75 in quarters and loonies. She has one quarter more than three-fourths the number of loonies, how many coins of each type does she have. I have tried this

Question 158293: Susan has saved $85.75 in quarters and loonies. She has one quarter more than three-fourths the number of loonies, how many coins of each type does she have.
I have tried this a zillion times using 2 separate equations and the elimination method a variety of ways, but cannot seem to get an answer that fits back. If someone can show me the proper equation to be using please then I can solve from there.
Thanks.
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Susan has saved $85.75 in quarters and loonies. She has one quarter more than three-fourths the number of loonies, how many coins of each type does she have.
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I believe a "looney" is one dollar. If that is right you get the following
equations:
Value Equation: 25Q + 100L = 8575
Quantity Equation: Q = (3/4)L + 1
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Rearrange the equations:
4Q - 3L = 4
25Q + 100L = 8575
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Multiply the 1st equation by 25; Multiply the 2nd equation by 4.
100Q - 75L = 100
100Q + 400L = 4*8575
----------------------
Subtract the 1st equation from the 2nd to get:
475L = 4*8575 - 100
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I don't have a calculator with me so I'll leave solving "L"
to you. When you get "L" substitute into one of the early
equation to solve for Q.
--------------------------
Cheers,
Stan H.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
"Susan has saved $85.75 in quarters and loonies" __ .25Q+1L=85.75 __ 25Q+100L=8575

"She has one quarter more than three-fourths the number of loonies" __ Q=.75L+1 __ 100Q=75L+100

***SOLUTION HERE***

multiplying 1st eqn by 4 __ 100Q+400L=34300 __ substituting __ (75L+100)+400L=34300

475L=34200 __ L=72

substituting __ .25Q+(72)=85.75 __ .25Q=13.75 __ Q=55
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