Question

Robert had $1.65 in dimes and quarters. The number of dimes he has is 3 more than twice the number of quarters he has. What system of equations could be used to find the number of quarters (q) and dimes (d) that he has?

Answer 1

A system of equations to find the number of quarters (q) and dimes (d) can be set up as: 0.10d + 0.25q = 1.65 and d = 2q + 3. By substituting the second equation into the first, you can solve for q and then find d.

Step-by-step explanation:

To find the number of quarters (q) and dimes (d) Robert has, we can set up a system of equations using the information given:

1. The total amount of money from dimes and quarters is $1.65.
2. The number of dimes is 3 more than twice the number of quarters.

These statements can be represented by the following two equations:

• 0.10d + 0.25q = 1.65 (the value equation representing the total amount of money)
• d = 2q + 3 (the relationship equation representing the number of dimes in terms of quarters)

Substituting the second equation into the first gives us:

• 0.10(2q + 3) + 0.25q = 1.65

Then, we can solve for q to find the number of quarters, and afterward, find the number of dimes by plugging the value of q back into the second equation.