Solve the problem.
-Michael's bank contains only nickels, dimes, and quarters. There are 51 coins in all, valued at $3.95. The number of nickels is 1 short of being three times the sum of the number of dimes and quarters together. How many
Dimes are in the bank?
A) 8 dimes
B) 13 dimes
C) 5 dimes
D) 38 dimes

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 problem statement:1. $n + d + q = 51$ (total coins)2. $0.05n + 0.10d + 0.25q = 3.95$ (total value)3. $n = 3(d + q) - 1$ (relationship between nickels, dimes, and quarters)Substituting $n$ from equation 3 into equation 1 gives $3(d + q) - 1 + d + q = 51$, simplifying to $4d + 4q = 52$, or $d + q = 13$.Substituting $n$ from equation 3 into equation 2 and using $d + q = 13$, we can solve for the exact numbers of dimes and quarters, eventually finding that there are 8 dimes in the bank.

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