Question

An office supply store recently sold a black printer ink cartridge for $17.99 and a color printer ink cartridge for $20.99. At the start of a recent fall

semester, a total of 59 of these cartridges was sold for a total of $1118.41. How many of each type were purchased?

Answer 1

40 black ink cartridges and 19 colored ink cartridges

Explanation:

Let
`b` represent the number of black printer ink cartridges sold. Let
`c` represent the number of color printer ink cartridges sold.

Set up a system of equations:

`\displaystyle\\\begin{cases}b+c=59\\17.99b+20.99c=1,118.41\end{cases}`

`b+c=59\implies b=59-c`

Substitute:

`\displaystyle\\17.99(59-c)+20.99c=1,118.41\\\implies c=\boxed{19}`

`\implies b+19=59\implies b=\boxed{40}`

⇒ 40 black ink cartridges, 19 colored ink cartridges (ans)