SOLUTION: toni has a collection of dimes & quarters with a face value of $25.30. She has 27 more quarters than dimes. How many of each coin does she have?

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Question 255460: toni has a collection of dimes & quarters with a face value of $25.30. She has 27 more quarters than dimes. How many of each coin does she have?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
With money problems you have to keep track of the count of each type of coin as well as their value.
d = number of dimes
10d = value of the dimes in cents
q = number of quarters
25q = value of quarters in cents
$25.30 = 2530 cents (because you need to convert everything to cents)
10d + 25q = 2530
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We also know she has 27 more quarters than dimes.
q = d + 27
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Substituting q = d+27 into the total value equation, we have:
10d + 25(d+27) = 2530
10d + 25d + 675 = 2530
35d = 1855
d = 53
.
q = d + 27
q = 53 + 27
q = 80
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Check the values
10d = 530
25q = 2000
10d + 25q = 2530
Checks.
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So she has 53 dimes and 80 quarters.
.
Done.