SOLUTION: A boy has only dimes and quarters in his piggy bank. If he has 60 coins worth 12 dollars and 45 cents altogether, how many quarters does he have in his bank?

Question 869045: A boy has only dimes and quarters in his piggy bank. If he has 60 coins worth 12 dollars and 45 cents altogether, how many quarters does he have in his bank?

Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Set q = number of quarters
d = number of dimes
($0.25 * q ) + ($0.10 * d ) = $12.45
0.25q + 0.10d = 12.45
multiply each side by 100
25q + 10d = 1245
We also know that q + d = 60
If we add -d to each side
q + d - d = 60 - d
q = 60 - d
Substitute (60 - d) for q in 25q + 10d = 1245
25(60 - d) + 10d = 1245
1500 - 25d + 10d = 1245
1500 -15d = 1245
add -1500 to each side
-15d = -255
divide each side by -15
d = -255/-15
d = 17
Since q + d = 60
q + 17 = 60
add -17 to each side
q = 43
43 quarters is $10.75
17 dimes is $1.70
$10.75 + $1.70 = $12.45 so we have a good solution
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