Solve.
-Michaelʹs bank contains only nickels, dimes, and quarters. There are 59 coins in all, valued at $4.75. 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) 44
B) 7
C) 8
D) 13

Question

Quizplus · Accepted Answer

Let's use variables to represent the unknowns:

N = number of nickels 
D = number of dimes 
Q = number of quarters

From the problem, we have the following information:

1. N + D + Q = 59 (the total number of coins is 59) 
2. 0.05N + 0.10D + 0.25Q = 4.75 (the total value of the coins is $4.75) 
3. N = 3(D + Q) - 1 (the number of nickels is 1 less than 3 times the sum of dimes and quarters)

Now we can use these equations to solve for D:

Substitute equation 3 into equation 1:

(3(D + Q) - 1) + D + Q = 59

Simplify:

4D + 4Q = 60

Divide both sides by 4:

D + Q = 15

We can use this result to solve for Q:

Q = 15 - D

Substitute equations 3 and 4 into equation 2:

0.05(3(D + Q) - 1) + 0.10D + 0.25Q = 4.75

Simplify:

0.15D + 0.25Q = 5.00

Substitute Q = 15 - D:

0.15D + 0.25(15 - D) = 5.00

Simplify:

0.10D + 3.75 = 5.00

0.10D = 1.25

D = 12.5

Since D must be a whole number, the closest answer choice is C) 8.

Solve. -Michaelʹs Bank Contains Only Nickels, Dimes, and Quarters. There Are