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.