Question

A home improvement store sold 255 air filters in one month. They sold size-A filters for $12.99 and size-B filters for $18.99. The store made $3,906.45 from this sale. Which equation will help to determine the number of size-A filters (A) and size-B filters (B) sold during the month?

A. A + B = 3,906.45
B. 12.99A + 18.99B = 255
C. 12.99A + 18.99B = 3,906.45
D. 18.99A + 12.99B = 3,906.45

Answer 1

To find the number of size-A and size-B filters sold, we use a system of equations: A + B = 255 for the total number of filters, and 12.99A + 18.99B = 3,906.45 for the total revenue. The correct equation representing the total revenue is C. 12.99A + 18.99B = 3,906.45.

Step-by-step explanation:

The equation that will help to determine the number of size-A filters (A) and size-B filters (B) sold during the month is based on the two pieces of information provided: the total number of filters sold (255) and the total amount of revenue generated ($3,906.45). The two types of filters were sold at different prices ($12.99 for size-A and $18.99 for size-B).

First, we know that the sum of the two types of filters sold equals the total number of filters sold. Thus, our first equation is:
A + B = 255.

Secondly, the total revenue from selling both types of filters should add up to the total revenue reported. Therefore, our second equation, based on the prices of the filters, is:
12.99A + 18.99B = 3,906.45.

Combining these two equations, we can solve for A and B using methods such as substitution or elimination. This system of equations is represented by:

• A + B = 255
• 12.99A + 18.99B = 3,906.45

Hence, the correct choice is C. 12.99A + 18.99B = 3,906.45.