How many 16oz cups did Samantha fill?

Question

Samantha works at a coffee shop where a 12oz cup costs $1.40, a 16oz cup costs $1.60 and a 20oz cup costs $1.70.
During a busy lunchtime, Samantha served 55 cups of coffee, emptying six 144oz coffee brewers while collecting a total of $85.90.
How many 16oz cups did Samantha fill?

Answer 1

25 of 16oz cups

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12oz cup - x,
16oz cup - y,
20oz cup -z

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x+y+z=55 --------------> (1)
12x+16y+20z=6*144 => 3x+4y+5z=216 --------------> (2)
1.4x+1.6y+1.7z=85.90 => 14x+16y+17z=859 --------------> (3)

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(3)- 14*(1) => 2y+3z=89 --------------> (4)
(2) - 3*(1) => y+2z=51 --------------> (5)
2*(5) - (4) => z=13, then using (5) and (1) we find y=25 and x=17