office supply algebra

Question

An office supply store recently sold a black printer ink cartridge for $18.99 and a color printer ink cartridge for $27.99. At the start of a recent fall semester, a total of 49 of these cartridges was sold for a total of $1146.51. How many of each type were purchased?

Answer 1

Let B be the number of Black printer ink cartridges and C be the number of color printer ink cartridges.

 

49 were sold in total, hence,

 

B+C= 49 ------------(1)

 

Also, its given that

 

18.99 B + 27.99 C = 1146.51---------(2)

Multiplying  (1) by 18.99,

 

18.99 B+ 18.99 C= 930.51 ------(3)

 

Now, subtracting  (3) from (2),

 

18.99 B + 27.99 C = 1146.51

18.99 B+ 18.99 C= 930.51

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                 9 C   =  216

                    C= 24

 

We know, B+ C= 49

Hence B = 49-24 = 25

 

Hence, number of Black printer ink cartridges = 25 and color printer ink cartridges = 24.