Question

An office supply store recently sold a black printer ink cartridge for $16.99 and a color printerink cartridge for $21.99. At the start of a recent fall semester, a total of 47 of these cartridgeswas sold for a total of $908.53. How many of each type were purchased?

Answer 1

Given:

The cost of a black printer ink cartridge is $16.99.

The cost of a colour printer ink cartridge is $21.99.

A total of 47 of these cartridges were sold for a total of $908.53.

To find:

The number of items sold in each type.

Step-by-step explanation:

Let x be the number of a black printer ink cartridge.

Let y be the number of a colour printer ink cartridge.

According to the question,

`\begin{gathered} x+y=47.............(1) \\ 16.99x+21.99y=908.53.............(2) \end{gathered}`

Multiplying 16.99 in equation (1), we get

`16.99x+16.99y=798.53...........(3)`

Subtract (3) from (2), we get

`\begin{gathered} 5y=110 \\ y=22 \end{gathered}`

Substitute in equation (1) we get,

`\begin{gathered} x+22=47 \\ x=47-22 \\ x=25 \end{gathered}`

Thus,

The number of a black printer ink cartridge is 25.

The number of a colour printer ink cartridge is 22.

Final answer:

• The number of a black printer ink cartridge is 25.

,

• The number of a colour printer ink cartridge is 22.