Sarah has 12 coins (nickels, dimes, and quarters) in her piggy bank with a total value of $1.65. There are 2 more dimes than nickels. How many of each type of coin does Sarah have?
A) 2 nickels, 8 dimes, and 3 quarters
B) 3 nickels, 5 dimes, and 4 quarters
C) 0 nickels, 4 dimes, and 5 quarters
D) 4 nickels, 7 dimes, and 3 quarters

Question

Quizplus · Accepted Answer

Let x be the number of nickels.
Then the number of dimes is x+2 and the number of quarters is 12-x-(x+2)=10-2x.
The value of the nickels is 0.05x, the value of the dimes is 0.1(x+2)=0.1x+0.2, and the value of the quarters is 0.25(10-2x)=2.5-0.5x.
The total value is $1.65, so we have the equation:
0.05x+0.1x+0.2+2.5-0.5x = 1.65
0.05x+0.5 = 1.65
0.05x = 1.15
x = 23
Therefore, Sarah has 3 nickels, 5 dimes, and 4 quarters, which is choice B.

Sarah Has 12 Coins (Nickels, Dimes, and Quarters) in Her