SOLUTION: A coin collection contains nickels, dimes, and quarters. There are twice as many dimes as quarters and nine more nickels than dimes. The total value of all the coins is $4.85. How
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-> SOLUTION: A coin collection contains nickels, dimes, and quarters. There are twice as many dimes as quarters and nine more nickels than dimes. The total value of all the coins is $4.85. How
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Question 1098754: A coin collection contains nickels, dimes, and quarters. There are twice as many dimes as quarters and nine more nickels than dimes. The total value of all the coins is $4.85. How many quarters are in the collection? Answer by ikleyn(52770) (Show Source):
Let "x" = the number of quarters.
Then the number of dimes is 2x, and the number of nickels is (2x+9).
Quarters contribute 25x cents to the total.
Dimes contribute 10*(2x) cents to the total.
Nickels contribute 5*(2x+9) cents to the total.
Thus the total is 25x + 10*(2x) + 5*(2x+9) cents.
From the other side, it is 485 cents.
It gives you an equation
25x + 10*(2x) + 5*(2x+9) = 485.
Simplify and solve for x:
25x + 20x + 10x + 45 = 485 ====> 55x = 485 - 45 = 440 ====> x = = 8.
Anser. 8 quarters, 16 dimes and 2*8+9 = 25 nickel.
Check. 8*25 + 16*10 + 25*5 = 485. ! Correct !
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