Question

Alexandra has 36 coins valued at six dollars, consisting of nickels (n) and quarters (q). Which equation can be used to solve for the numbers of nickels and quarters?

A) n + q = 36 and 0.05n + 0.25q = 6
B) n - q = 36 and 0.05n - 0.25q = 6
C) n + q = 36 and 0.05n - 0.25q = 6
D) n - q = 36 and 0.05n + 0.25q = 6

Answer 1

The correct equations to solve for the numbers of nickels and quarters that Alexandra has are n + q = 36 and 0.05n + 0.25q = 6, as they represent the total number of coins and their total value, respectively.

Step-by-step explanation:

The question involves finding the number of nickels (n) and quarters (q) Alexandra has if she has a total of 36 coins valued at six dollars. To solve for the numbers of nickels and quarters, we need to establish two equations: one for the number of coins and the other for the total value of the coins.

The first equation is based on the number of coins:

• n + q = 36

which indicates that the sum of the number of nickels and the number of quarters equals 36 coins.

The second equation is based on the total value of the coins:

• 0.05n + 0.25q = 6

where 0.05n represents the value of the nickels and 0.25q represents the value of the quarters, with the total value being six dollars.

Therefore, the correct equation to use to solve for the numbers of nickels and quarters is:

A) n + q = 36 and 0.05n + 0.25q = 6