Question 1010918: In a collection box , there are dimes and quarters whose total value is $28. If there were as many quarters as there are dimes , and as many dimes as there are quarters , the total value would be $36.40. How many coins of each kind are in the collection box ?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! d = no. of dimes
q = no. of quarters
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Write an equation for each statement
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In a collection box , there are dimes and quarters whose total value is $28.
.10d + .25q = 28.00
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If there were as many quarters as there are dimes , and as many dimes as there are quarters , the total value would be $36.40.
.25d + .10q = 36.40
multiply by 2.5 and subtract the 1st equation
.625d + .25q = 91.00
.10d + .25q = 28.00
-----------------------subtraction eliminates q, find d
.525d + 0 = 63
d = 63/.525
d = 120 dimes
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Use the 1st equation to find the no. of quarters
.10(120) + .25q = 28
12 + .25q = 28
.25q = 28 - 12
.25q = 16
q = 16/.25
q = 64 quarters
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Confirm this in the 2nd equation
.25(120) + .10(64) =
30.00 + 6.40 = 36.40
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