Final answer:
To solve this problem, set up a system of equations with two conditions. Then, solve the system by eliminating one variable and substituting it into the second equation. The solution is 8 dimes and 17 quarters.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's say the number of dimes is 'x' and the number of quarters is 'y'. We have two conditions:
- The total value of the dimes and quarters is $5, so we have the equation 0.10x + 0.25y = 5.
- The total number of coins is 25, so we have the equation x + y = 25.
Now, we can solve this system of equations. Multiply the second equation by 0.10 to get 0.10x + 0.10y = 2.50. Subtract this equation from the first equation to eliminate 'x': 0.10x + 0.25y - (0.10x + 0.10y) = 5 - 2.50. Simplifying, we get 0.15y = 2.50. Divide both sides by 0.15 to solve for 'y': y = 16.67 (rounded to the nearest whole number, y = 17). Substitute this value of 'y' into the second equation to solve for 'x': x + 17 = 25, x = 8. So, there are 8 dimes and 17 quarters.