Question

A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85.

Which system of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?

Answer 1

Let's define the two variables as follows:
- q = number of quarters
- d = number of dimes

Since we have 18 coins in total, the first equation can be written to represent the total number of coins, which is:

1. q + d = 18

Each quarter is worth $0.25 and each dime is worth $0.10. The total value of the coins is $2.85. So the second equation can be written to represent the total value of the coins:

2. 0.25q + 0.10d = 2.85

Now we have a system of two equations with two variables:

{
q + d = 18
0.25q + 0.10d = 2.85
}

This system can be used to determine the number of quarters (q) and the number of dimes (d) in the bag.