An office supply store recently sold a black printer ink cartridge for $14.99 and a color printer ink cartridge for $27.99. At start of a recent fall semester, a total of 49 of these cartidges was sold for a total of $1046.51. How many of each type were purchased?

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jitumahi76 jitumahi76 · Answer 1 · 2019-12-15T11:38:02+01:00

Answer:

25 black printer ink cartridge and 24 color printer ink cartridge were purchased.

Step-by-step explanation:

Let the number of black printer ink cartridge be x

Also Let the number of color printer ink cartridge be y

Total number of cartridges were =49

Hence;

[tex]x+y=49 \ \ \ \ equation \ 1[/tex]

Also;

Cost of black printer ink cartridge = $14.99

Cost of color printer ink cartridge = $27.99

Total Money after selling both = $1046.51

Hence, the equation can be framed as;

[tex]14.99x+27.99y=1046.51[/tex]

Now Multiplying both side by 100 we get;

[tex]100(14.99x+27.99y)=1046.51\times100\\100\times 14.99x +100\times 27.99y = 104651\\1499x+2799y = 104651 \ \ \ \ equation \ 2[/tex]

Now multiplying equation 1 by 1499 we get;

[tex]1499x + 1499y = 73451\ \ \ \ equation \ 3[/tex]

Now Subtracting equation 3 from equation 2 we get;

[tex]1300y = 31200\\y = \frac{31200}{1300} = 24[/tex]

Now Substituting value if y in equation 1 we get;

[tex]x+y=49\\x+24 = 49\\x = 49-24\\x =25[/tex]

Hence 25 black printer ink cartridge and 24 color printer ink cartridge were purchased.