Answer:
Jasper has 24 quarters and 26 dimes in his coin collection.
Explanation:
Let's assume Jasper has "q" quarters and "d" dimes in his collection.
According to the problem, he has a total of 50 coins, so we can write the equation:
q + d = 50
The value of a quarter is $0.25, and the value of a dime is $0.10. We are told that the total value of the coins is $8.60, so we can write another equation:
0.25q + 0.10d = 8.60
Now we have a system of two equations:
q + d = 50
0.25q + 0.10d = 8.60
To solve this system, we can use substitution or elimination. Let's use substitution.
We rearrange the first equation to solve for q:
q = 50 - d
We substitute this expression for q in the second equation:
0.25(50 - d) + 0.10d = 8.60
Simplifying the equation:
12.50 - 0.25d + 0.10d = 8.60
Combining like terms:
-0.15d = 8.60 - 12.50
-0.15d = -3.90
Dividing both sides of the equation by -0.15 to solve for d:
d = (-3.90) / (-0.15)
d = 26
We found that Jasper has 26 dimes.
Substituting the value of d back into the first equation to solve for q:
q + 26 = 50
q = 50 - 26
q = 24
We found that Jasper has 24 quarters.
Therefore, the solution is that Jasper has 24 quarters and 26 dimes in his coin collection.