Michael's bank contains only nickels, dimes, and quarters. There are 62 coins in all, valued at $\$$ 5.20. The number of nickels is 10 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?
A) 44
B) 8
C) 10
D) 15

Question

Quizplus · Accepted Answer

Let the number of dimes be $x$, and the number of quarters be $y$. Then the number of nickels is $3(x+y)-10$. Since there are 62 coins in all, we have:$$x+y+3(x+y)-10=62$$Simplifying:$$4x+4y=72$$$$x+y=18$$Since the total value of the coins is $\$$ 5.20, we have:$$0.10x+0.25y=5.20$$Simplifying:$$2x+5y=104$$Solving the system of equations, we get:$$x=10$$Therefore, there are 10 dimes in the bank.

Michael's Bank Contains Only Nickels, Dimes, and Quarters $\$$ 520 the Number of Nickels Is 10 Short of Being