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