Question

A jar contains nickels and dimes. There is a total of 200 coins in the jar and their value is $14.55. How many dimes are in the jar?

Answer 1

To find out the number of dimes in the jar, we set up a system of linear equations using the total number of coins and the total value in dollars. After simplifying and solving the equations, we find that there are 91 dimes in the jar.

Step-by-step explanation:

Step-by-Step Solution

We are dealing with a system of linear equations to determine the number of nickels and dimes in a jar. First, let's establish the equations based on the given information:

• Let n represent the number of nickels.
• Let d represent the number of dimes.

We know there are a total of 200 coins, so we have the equation:

n + d = 200

Also, the total value is $14.55. Nickels are worth 5 cents, and dimes are worth 10 cents, so the second equation is:

5n + 10d = 1455 (since we are using cents).

Solving the system:

1. Multiply the first equation by 5 to align the nickel terms
2. 5n + 5d = 1000
3. Subtract this new equation from the second equation to eliminate n:
4. (5n + 10d) - (5n + 5d) = 1455 - 1000
5. 5d = 455
6. Divide by 5 to solve for d:
7. d = 91

There are therefore 91 dimes in the jar.

Answer 2

This is the answer to the question