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Deangelo has $7 worth of dimes and quarters in a jar. He has 7 more quarters than dimes.

How many of each coin does he have?

____Dimes _____Quarters

1 Answer

4 votes

Let's use a system of equations to solve this problem. Let D represent the number of dimes and Q represent the number of quarters.

We have two pieces of information:

Deangelo has $7 worth of dimes and quarters, and the value of a dime is $0.10, and the value of a quarter is $0.25. So we can write the equation for the total value as:

0.10D + 0.25Q = 7

Deangelo has 7 more quarters than dimes, which can be expressed as:

Q = D + 7

Now, we can solve this system of equations.

First, let's substitute the value of Q from the second equation into the first equation:

0.10D + 0.25(D + 7) = 7

Now, distribute the 0.25 on the left side:

0.10D + 0.25D + 1.75 = 7

Combine like terms:

0.35D + 1.75 = 7

Now, subtract 1.75 from both sides of the equation:

0.35D = 7 - 1.75

0.35D = 5.25

Now, divide by 0.35 to solve for D:

D = 5.25 / 0.35

D = 15

So, Deangelo has 15 dimes.

Now, we can find the number of quarters using the second equation:

Q = D + 7

Q = 15 + 7

Q = 22

So, Deangelo has 22 quarters.

Therefore, Deangelo has 15 dimes and 22 quarters.

User MarkeD
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