SOLUTION: A newspaper carrier has $4.10 in change. He has four more quarters than dimes but two times as many nickels as quarters. How many coins of each type does he have?
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Question 1050880: A newspaper carrier has $4.10 in change. He has four more quarters than dimes but two times as many nickels as quarters. How many coins of each type does he have? Answer by ikleyn(52858) (Show Source):
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A newspaper carrier has $4.10 in change. He has four more quarters than dimes but two times as many nickels as quarters.
How many coins of each type does he have?
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Let Q be the number of quarters.
Then the number of dimes is (Q-4) ("He has four more quarters than dimes")
and the number of nickels is 2Q.
Quarters contribute 25*Q cents to the total.
Dimes contribute 10*(Q-4) cents to the total.
Nickels contribute 5*(2Q) cents to the total.
The "value" equation is
25Q + 10*(Q-4) + 5*(2Q) = 410 cents, or
25Q + 10Q - 40 + 10Q = 410, or
25Q + 10Q + 10Q = 410 + 40, or
45Q = 450 ---> Q = = 10.
Answer. 10 quarters, 25-4 = 21 dimes and 20 nickels.
