SOLUTION: Sam found a number of nickels, dimes and quarters in his room. He found 3 more dimes than nickels but twices as many quarters as dimes. The total value of the coins was $5.05. How
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Question 167769: Sam found a number of nickels, dimes and quarters in his room. He found 3 more dimes than nickels but twices as many quarters as dimes. The total value of the coins was $5.05. How many coins of each type did Sam find? Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! Sam found a number of nickels, dimes and quarters in his room. He found 3 more dimes than nickels but twice as many quarters as dimes. The total value of the coins was $5.05. How many coins of each type did Sam find?
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Let n = number of nickels
then from "He found 3 more dimes than nickels"
n+3 = number of dimes
and from "twice as many quarters as dimes"
2(n+3) = number of quarters
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From the total we get:
5.05 = .05n + .10(n+3) + .25(2(n+3))
5.05 = .05n + .10n + .3 + .25(2n+6)
5.05 = .05n + .10n + .3 + .50n + 1.5
5.05 = .15n + .3 + .50n + 1.5
5.05 = .65n + .3 + 1.5
5.05 = .65n + 1.8
3.25 = .65n
5 = n (number of nickels)
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dimes:
n+3 = 5+3 = 8 (number of dimes)
.
quarters:
2(n+3) = 2(5+3) = 2(8) = 16 (number of quarters)
