Question

Amy has 18 coins consisting of nickels, dimes, and quarters. She has the same amount of nickels as quarters. How many of each coin does she have if the value of the coins is $2.20?

Responses

Answer 1

Amy has 7 nickels, 1 dime, and 7 quarters.

Step-by-step explanation:

Let's solve this problem by setting up a system of equations. Let's say the number of nickels is N, the number of dimes is D, and the number of quarters is Q.

Since Amy has the same amount of nickels as quarters, we can write the equation N = Q.

Now, let's set up another equation based on the total value of the coins.

The value of a nickel is 5 cents, the value of a dime is 10 cents, and the value of a quarter is 25 cents. So the equation can be written as

5N + 10D + 25Q = 220 cents.

Since we have two equations and two variables, we can solve for N and Q.

Using the first equation, we substitute Q for N in the second equation, giving us

5N + 10D + 25N = 220 cents.

Simplifying this equation, we get

30N + 10D = 220.

Now, we can substitute in a value for D and solve for N and Q. Let's say D = 1.

Plugging in this value, we get 30N + 10(1) = 220. Solving for N, we get N = 7.

Since N = Q, we also know that Q = 7.

Therefore, Amy has 7 nickels, 1 dime, and 7 quarters.