Bill has $2.00 in quarters and dimes. the number of quarters is 4 less than twice the number of dimes. find the number of coins of each type

Define your variables:

Q: number of quarters

D: number of dimes

Next, create your equations

Q = 2D-4

25Q+10D=200

Because one variable (Q) is already written in terms of the other variable, D, you can already start solving with substitution.

25 (2D-4) + 10D=200

50D-100+10D=200

60D=300

D=5

Substitute D back into the other equation to find Q.

Q=2D-4

Q=2 (5) - 4

Q=6

Substitute D and Q into the second equation to check.

25Q+10D=200

25 (6) + 10 (5) = 200

150+50=200

This works, so the answer is right! Bill has 6 quarters and 5 dimes.