Question

Juanita paid for an item at the store and received seven dollars in change. She received three more dimes than she did nickels and three more quarters than she did dimes. How many nickels, dimes and quarters did she receive?

Answer 1

Step-by-step explanation: Let's use a system of equations to solve this problem.

Let N represent the number of nickels, D represent the number of dimes, and Q represent the number of quarters.

We have three pieces of information:

Juanita received seven dollars in change, which is equal to 700 cents, so we can write the equation:

5N + 10D + 25Q = 700 (since 1 dollar = 100 cents)

Juanita received three more dimes than nickels, which can be expressed as:

D = N + 3

Juanita received three more quarters than dimes, which can be expressed as:

Q = D + 3

Now, we can solve this system of equations. We'll start with the third equation:

Q = D + 3

Next, substitute this expression for Q into the second equation:

D = N + 3

Now, substitute both of these expressions into the first equation:

5N + 10(N + 3) + 25(D + 3) = 700

Now, simplify and solve for N:

5N + 10N + 30 + 25D + 75 = 700

15N + 25D + 105 = 700

15N + 25D = 700 - 105

15N + 25D = 595

Now, divide by 5 to simplify:

3N + 5D = 119

We have two equations now:

D = N + 3

3N + 5D = 119

Let's solve this system of equations. We can start by substituting the value of D from the first equation into the second equation:

3N + 5(N + 3) = 119

Now, distribute the 5 on the left side:

3N + 5N + 15 = 119

Combine like terms:

8N + 15 = 119

Subtract 15 from both sides:

8N = 119 - 15

8N = 104

Now, divide by 8:

N = 104 / 8

N = 13

So, there are 13 nickels.

Now, you can find the number of dimes and quarters using the relationships given earlier:

D = N + 3

D = 13 + 3

D = 16

There are 16 dimes.

Q = D + 3

Q = 16 + 3

Q = 19

There are 19 quarters.

To summarize:

Juanita has 13 nickels.

She has 16 dimes.

She has 19 quarters.