Final answer:
To find out how many dimes and quarters the grandson has, we set up two equations based on the given information and solve the system of equations. The grandson has 60 quarters and 100 dimes.
Step-by-step explanation:
To solve how many dimes and quarters the grandson has that total $25, with 40 more dimes than quarters, we can use a system of equations. Let's define d as the number of dimes and q as the number of quarters. We are told that the total value of the coins is $25, which can be written as the equation 0.10d + 0.25q = 25. We also know that there are 40 more dimes than quarters, which gives us the second equation, d = q + 40.
By substituting the second equation into the first, we get:
- 0.10(q + 40) + 0.25q = 25
- 0.10q + 4 + 0.25q = 25
- 0.35q + 4 = 25
- 0.35q = 21
- q = 21 / 0.35
- q = 60 (quarters)
Now we can find the number of dimes:
- d = q + 40
- d = 60 + 40
- d = 100 (dimes)
Therefore, the grandson has 60 quarters and 100 dimes.