Question

Kyle works at a donut​ factory, where a​ 10-oz cup of coffee costs 95cents¢​, a​ 14-oz cup costs​ $1.15, and a​ 20-oz cup costs​ $1.50. During one busy​ period, Kyle served 35 cups of​ coffee, using 544 ounces of​ coffee, while collecting a total of ​$43.60 How many cups of each size did Kyle​ fill

Answer 1

Let s, m, L represent the number of small, medium, and Large cups of coffee Kyle filled.
  s +m +L = 35 . . . . . . . . . . . . . . . served 35 cups
  10s +14m +20L = 544 . . . . . . . . using 544 ounces of coffee
  .95s +1.15m +1.50L = 43.60 . . . while collecting $43.60

Solving these 3 linear equations in 3 unknowns by your favorite method, you find
  Kyle filled 6 small cups (10 oz)
  Kyle filled 16 medium cups (14 oz)
  Kyle filled 13 Large cups (20 oz)

_____
Elimination is a reasonable way to start. Subtract 10 times the first equation from the second, and 0.95 times the first equation from the third. Then you have
  4m +10L = 194
  .2m +.55L = 10.35
Now, you can subtract .05 times the first of these equation from the last to get
  .05L = .65
  L = 13
Back-substituting gets you the values of the other variables.