Solve.
-Michael's bank contains only nickels, dimes, and quarters. There are 68 coins in all, valued at $5.70. The number of nickels is 8 short of being three times the sum of the number of dimes and quarters together. How many Dimes are in the bank?
A)10
B)9
C)49
D)15

Question

Quizplus · Accepted Answer

Let the number of dimes be D, quarters be Q, and nickels be N. We have three equations based on the given information:1. $N + D + Q = 68$ (total coins)2. $5N + 10D + 25Q = 570$ (total value in cents)3. $N = 3(D + Q) - 8$ (relationship between nickels, dimes, and quarters)Substituting the third equation into the first gives us $3(D + Q) - 8 + D + Q = 68$, simplifying to $4D + 4Q = 76$, or $D + Q = 19$.Using equations 1 and 3, we can solve for D by substituting values and simplifying the equations. The correct number of dimes, based on the given conditions and solving the system of equations, is 10.

Solve. -Michael's Bank Contains Only Nickels, Dimes, and Quarters. There Are