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Jasper has a coin collection consisting of quarters and dimes. He has 50 coins worth $8.60. How many

of each coin does he have? Write the solution in a complete sentence.

User Alix Axel
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1 Answer

7 votes

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.

User M Abbas
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