Solve.
-Michael's bank contains only nickels, dimes, and quarters. There are 66 coins in all, valued at $5.40. The number of nickels is 6 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)10
C)48
D)15

Question

Quizplus · Accepted Answer

Let's use N, D, and Q to represent the number of nickels, dimes, and quarters, respectively. We know that:
N + D + Q = 66 ---------(1)
0.05N + 0.1D + 0.25Q = 5.40 -------(2)
N = 3(D + Q) - 6 ---------(3)

We can use equation (3) to substitute for N in both equations (1) and (2):
3(D + Q) - 6 + D + Q = 66
4D + 4Q = 72
D + Q = 18

0.05(3D + 3Q - 6) + 0.1D + 0.25Q = 5.4
0.15D + 0.15Q - 0.3 + 0.1D + 0.25Q = 5.4
0.25D + 0.4Q = 5.7

Now we have two equations with two unknowns (D and Q). We can use substitution or elimination to solve for them. Let's use elimination:
4D + 4Q = 72 ⇒ D + Q = 18
0.25D + 0.4Q = 5.7 ⇒ 25D + 40Q = 570

Multiplying the first equation by 25, we get:
25D + 25Q = 450

Subtracting this equation from the second equation, we eliminate D:
15Q = 120
Q = 8

Now we know that there are 8 quarters in the bank. Using equation (1), we can find the number of dimes:
D + Q = 18
D = 18 - Q
D = 10

Therefore, there are 10 dimes in the bank. Answer: B)10

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