Question

Frank has $2.40 in nickels and

dimes. In total he has 40 coins,
how many are nickels and how
many are dimes?
(A) 10 nickels
30 dimes
C.) 8 nickels
32 dimes
B.) 32 nickels
8 dimes
D.) 30 nickels
10 dimes

Answer 1

By setting up simultaneous equations and solving algebraically, we have calculated that Frank has 32 nickels and 8 dimes, which gives him a total of 40 coins and equals $2.40 in value.

Step-by-step explanation:

Calculating Quantity of Nickels and Dimes

Let's solve this problem using algebra. We have two types of coins - nickels (5 cents each) and dimes (10 cents each) - and we need to find out how many of each Frank has. Let's denote the number of nickels as N and the number of dimes as D. The total amount of money in dollars is $2.40, which translates to 240 cents. We also know the total number of coins, which is 40.

So, we have two equations based on the given information:

1. N + D = 40 (total number of coins)
2. 5N + 10D = 240 (total value of coins in cents)

Now, let's solve these equations simultaneously. From equation 1:

N = 40 - D

Substitute the value of N from equation 1 into equation 2:

5(40 - D) + 10D = 240

200 - 5D + 10D = 240

5D = 240 - 200

5D = 40

D = 40 / 5

D = 8

Therefore, we have 8 dimes.

Now, plug the value of D back into equation 1 to find N:

N = 40 - 8

N = 32

So, Frank has 32 nickels and 8 dimes.

The correct answer is 32 nickels and 8 dimes.