Fred has $5.05 worth of coins floating around in his backpack, all of which are quarters and dimes. If there are 5 more dimes than quarters, how many

boitshupoO 2021-06-11 Answered
Fred has $5.05 worth of coins floating around in his backpack, all of which are quarters and dimes. If there are 5 more dimes than quarters, how many coins of each are there?

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Jaylen Fountain
Answered 2021-06-13 Author has 16931 answers
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question2answer
Answered 2021-08-04 Author has 28686 answers

Let q be the number of quarters and d be the number of dimes. Hecall that 1 quarter = 0.25 and 1 dime = 0.10
Fred has 5.05 consisting of quarters and dimes:
\(0.25q + 0.10d = 5.05\)
There are 5 more dimes than quarters:
\(d=q+5\)
Solve by substitution. Substitute (2) to (1) and solve for q: \(0.25q + 0.10(q + 5) = 5.05\)
\(0.25q + 0.10q + 0.50 = 5.05\)
\(0.35q + 0.50 = 5.05\)
\(0.35q = 4.55\)
\(q=13\)
Solve for d using (2):
\(d=13+5\)
\(d=18\)
Hence, Fred has 13 quarters and 18 dimes

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