# 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

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 Click here to see ALL problems on test 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(57214)   (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? ------ Quantity Equation: n + d + q = 105 coins Quantity Equation: d = (1/3)n + 5 Quantity Equation: q = 2d -------- Substitute for d and q and solve for "n": n + (1/3)n + 5 + 2d = 105 ------ (4/3)n + 5 + (2/3)n + 10 = 105 2n + 15 = 105 ------ 2n = 90 n = 45 (number of nickels) d = (1/3)n+5 = 15+5 = 20 (number of dimes) q = 2d = 40 (number of quarters) ================================== Cheers, Stan H.