Word problem ugh

Question

An office supply store recently sold a black printer ink cartridge for 18.99 and a color printer ink cartridge for 23.99. At the start of a recent fall semester a total of 55 of these cartridges was sold for a total of $ 1139.45. How many of each type were purchased?

Answer 1

These confused me when I first learned them. Let's do this.

b + c = 55

18.99b + 23.99c = 1139.45

The first thing I would do is solve the first equation for b or c. I'll do b.

b = 55 - c

Substitute!

18.99(55 - c) + 23.99c = 1139.45

1044.45 - 18.99c + 23.99c = 1139.45

5c = 95

c = 19 color cartridges

b = 55 - 19

b = 36 black cartridges