SOLUTION: Rita has a collection of 105 coins consisting of nickels, dimes, and quarters. The number of dimes is 5 more than one-third the number of nickels, and the number of quarters is twi

Question 461117: Rita has a collection of 105 coins consisting of nickels, dimes, and quarters. The number of dimes is 5 more than one-third the number of nickels, and the number of quarters is twice the number of dimes. How many coins of each kind does she have?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Rita has a collection of 105 coins consisting of nickels, dimes, and quarters. The number of dimes is 5 more than one-third the number of nickels, and the number of quarters is twice the number of dimes. How many coins of each kind does she have?
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Quantity Equation: n + d + q = 105 coins
Quantity Equation: d = (1/3)n + 5
Quantity Equation: q = 2d
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Substitute for d and q and solve for "n":
n + (1/3)n + 5 + 2d = 105
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(4/3)n + 5 + (2/3)n + 10 = 105
2n + 15 = 105
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2n = 90
n = 45 (number of nickels)
d = (1/3)n+5 = 15+5 = 20 (number of dimes)
q = 2d = 40 (number of quarters)
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Cheers,
Stan H.
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