Question

A vending machine only accepts quarters ($0.25) and nickels ($0.05). When the machine was emptied Friday afternoon, 325 coins were counted and had a value of $56.25. Which equations, when solved, gives the number of quarters, q, and the number of nickels, n ?

Answer 1

The equations that, when solved, give the number of quarters (q) and the number of nickels (n) are:

q + n = 325

0.25q + 0.05n = 56.25

Step-by-step explanation:

Let q be the number of quarters and n be the number of nickels.

The total number of coins is 325, so the first equation is:

q + n = 325

The value of the coins is $56.25, so the second equation is:

0.25q + 0.05n = 56.25

These two equations represent the system of linear equations that can be solved to find the values of q and n. The first equation accounts for the total number of coins, and the second equation represents the total value of the coins.

Therefore, the system of equations is q + n = 325 and 0.25q + 0.05n = 56.25.