Question

Dan has 50 coins that total $7.30. All of his coins are dimes, D, and quarters, Q. Write a system of equations that models this situation.

Answer 1

d + q = 50

0.10d + 0.25q = 7.30

Explanation:

Since all of the 50 coins are dimes and quarters, we can write the equation:

d + q = 50, where d is the number of dimes and q is the number of quarters

Now, we know that dimes are 10 cents, or $0.10 and quarters are 25 cents, or $0.25. So, if we multiply 0.10 by d, we get the total value of the dimes, and if we multiply 0.25 by q, we get the total value of the quarters. The total value of all dimes and quarters is 7.30, so we have the equation:

0.10d + 0.25q = 7.30

Thus, the system is:

d + q = 50

0.10d + 0.25q = 7.30

Answer 2

Explanation:

Step 1: Find the first equation

We need to make an equation to represent the amount of coins. Let dimes be represented with D and quarters with Q.

Q + D = 50

Step 2: Make the second equation

We need to make an equation to represent the total money together. So, let dimes be represented with 0.10D and quarters with 0.25Q.

0.10D + 0.25Q = 7.30

Step 3: Make the system of equations

Q + D = 50

0.10D + 0.25Q = 7.30