Lauren has a purse full of dimes and quarters. She has 25 less dimes than quarters. If she has a total of $10.45, which system of equations would she write to find the number of dimes, d and quarters, q?​

D(0.10) + Q(0.25) = 10.45

Q = D + 25 (or Q - D = 25)

Step-by-step explanation:

D = number of dimes

Q = number of quarters

D(0.10) + Q(0.25) = 10.45

Q = D - 25 (or D - Q = 25)

We multiply the number of dimes she has by $0.10, because that is the worth of each dime, and we multiply the number of quarters she has by $0.25 because that is the worth of each quarter. We then set that equal to $10.45, the overall value of her coins.

Because she has 25 less dimes than quarters, the number of dimes she has should be 25 less than the number of quarters she has. So the number of quarters she has should be equal to the number of dimes she has plus 25.