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
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.
