Michael's bank contains only nickels, dimes, and quarters. There are 64 coins in all, valued at $\$$ 5.40. The number of nickels is 4 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?
A) 8
B) 9
C) 13
D) 47

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. $n + d + q = 64$ (total coins)2. $5n + 10d + 25q = 540$ (total value in cents)3. $n = 3(d + q) - 4$ (relation between nickels, dimes, and quarters)From equation 3, we can express $n$ in terms of $d$ and $q$, and then substitute this expression into the other equations to solve for $d$ and $q$. Simplifying and solving the system of equations, we find that there are 8 dimes in the bank.

Michael's Bank Contains Only Nickels, Dimes, and Quarters $\$$ 540 the Number of Nickels Is 4 Short of Being