Nelson has seven coins. all the coins are dimes and quarters. he has a total of $1.15. how many dimes and how many quarters does he have

4 dimes, 3 quarters

Step-by-step explanation:

Given that there are two variables with two different relationships, you can set up a system of equations and use the substitution method to first solve for one variable and then the other:

d + q = 7

0.10d + 0.25q = 1.15

Solve for 'q' in the first equation:  q = 7 - d

Substitute the express '7 - d' for 'q' in the second equation:

0.10d + 0.25(7 - d) = 1.15

Distribute: 0.10d + 1.75 - 0.25d = 1.15

Combine like terms: 1.75 - 0.15d = 1.15

Subtract 1.75 from both sides: -0.15d = -0.6

Divide both sides by -0.15:  d = 4

Solve for q:  3 + q = 7 or q = 4