Question

A jar of nickels and dimes contains $6.75. There are 84 more nickels than dimes. How many of each are there?

A) 75 nickels and 60 dimes
B) 90 nickels and 6 dimes
C) 80 nickels and 40 dimes
D) 60 nickels and 24 dimes

Answer 1

There are 101 nickels and 17 dimes.

Step-by-step explanation:

Let's use a system of equations to solve this problem.

Let's say the number of nickels is represented by N and the number of dimes is represented by D.

From the given information, we can set up the following equations:

1. N = D + 84 (There are 84 more nickels than dimes)

2. 0.05N + 0.10D = 6.75 (The value of the nickels and dimes adds up to $6.75)

We can substitute the value of N from equation 1 into equation 2:

0.05(D + 84) + 0.10D = 6.75

0.05D + 4.20 + 0.10D = 6.75

0.15D + 4.20 = 6.75

0.15D = 2.55

D = 2.55 / 0.15

D = 17

Substitute the value of D back into equation 1:

N = 17 + 84

N = 101

Therefore, there are 101 nickels and 17 dimes.