SOLUTION: Please help, thank you. Kyle works at a donut​ factory, where a​ 10-oz cup of coffee costs 95¢​, a​ 14-oz cup costs​ $1.15, and a​ 20-oz cup

Algebra ->  Systems-of-equations -> SOLUTION: Please help, thank you. Kyle works at a donut​ factory, where a​ 10-oz cup of coffee costs 95¢​, a​ 14-oz cup costs​ $1.15, and a​ 20-oz cup       Log On


   

Question 1110484: Please help, thank you.
Kyle works at a donut​ factory, where a​ 10-oz cup of coffee costs 95¢​, a​ 14-oz cup costs​ $1.15, and a​ 20-oz cup costs​ $1.50. During one busy​ period, Kyle served 27 cups of​ coffee, using 424 ounces of​ coffee, while collecting a total of ​$34.00. How many cups of each size did Kyle​ fill? Kyle filled
​__10-oz cup(s),
​__14-oz cup(s), and
​__20-oz cup(s)
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
x of the small
y of the medium
z of the large

system%28x%2By%2Bz=27%2C10x%2B14y%2B20z=424%2C95x%2B115y%2B150z=3400%29

system%28x%2By%2Bz=27%2C5x%2B7y%2B10z=212%2C19x%2B23y%2B30z=680%29

system%28x%2By%2Bz=27%2C0%2B2y%2B5z=77%2C0%2B4y%2B11z=167%29

Subtract 2 times this second equation from the third equation:
highlight%28z=13%29

You can use the last system to find y and x.
highlight%28y=6%29
-
highlight%28x=8%29