# 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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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