SOLUTION: My piggy bank contains $19.75 in dimes and quarters, there are 100 coins in all, how many dimes are there? How do I solve this?

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Question 465846: My piggy bank contains $19.75 in dimes and quarters, there are 100 coins in all, how many dimes are there? How do I solve this?
Found 3 solutions by jorel1380, stanbon, scott8148:
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
d+q=100
10d+25q=1975
10d+10q=1000
15q=975
q=65
d=35
You have 35 dimes and 65 quarters..

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
My piggy bank contains $19.75 in dimes and quarters, there are 100 coins in all, how many dimes are there?
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Quantity Eq: d + q = 100
Value Eq:: 10d+25q = 1975 cents
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Multiply thru 1st by 25
25d + 25q = 25*100
10d + 25q = 1975
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Substract and solve for "d":
15d = 525
d = 35 (# of dimes)
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Cheers,
Stan H.
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Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
simultaneous equations

"$19.75 in dimes and quarters" ___ 10d + 25q = 1975

"there are 100 coins in all" ___ d + q = 100 ___ 25d + 25q = 2500

subtracting equations (to eliminate q) ___ 15d = 525