Question

You have 47 total coins for a total of $9.95. You only have quarters and dimes. How many of each coin do you have

Answer 1

The student has 35 quarters and 12 dimes, which can be determined through setting up a system of equations based on the total number of coins and their total value.

Step-by-step explanation:

To solve the problem of determining the number of quarters and dimes a student has when they have 47 coins for a total of $9.95, we can use a system of equations.

1. Let's call the number of quarters Q and the number of dimes D.
2. The first equation comes from the total number of coins: Q + D = 47.
3. The second equation comes from the total value of the coins: 0.25Q + 0.10D = 9.95.
4. Multiplying the second equation by 100 to eliminate decimals gives us 25Q + 10D = 995.
5. Now we can multiply the first equation by 10 to make subtraction easier: 10Q + 10D = 470.
6. Subtracting the new first equation from the modified second equation will give us the number of quarters: 15Q = 525, so Q = 35.
7. Substituting Q = 35 into the first equation gives us 35 + D = 47, so D = 12.

Thus, the student has 35 quarters and 12 dimes.

Answer 2

You have 35 quarters and 12 dimes