Question

michaels bank contains only nickels, dimes, and quarters. There are 63 coins in all, valued at $4.85. the number of nickels is 1 short of being 3 times the sum of the number of dimes and quarters together. how many dimes are in the bank?

Answer 1

25 dimes

Explanation:

Let n = nickels ($0.05)

Let d = dimes ($0.10)

Let q = quarters ($0.25)

n + d + q = 63

0.05n + 0.1d + 0.25q = 4.85

The number of nickels is 1 short of being 3 times the sum of the number of dimes and quarters together

n = 3(d + q) - 1

Substitute into the 1st equation

n + d + q = 63

3(d + q) - 1 + d + q = 63

3d + 3q - 1 + d + q = 63

4d + 4q - 1 = 63

4d + 4q = 64

d + q = 16

Substitue value of (d + q) into 3rd equation

n = 3(d + q) - 1

n = 3(16) - 1 = 47

Substitute the values of n and d + q into the 2nd equation

0.05(47) + 0.10d + 0.25(16) = 4.85

2.35 + 0.10d = 4.85

0.10d = 2.5

d = 25