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 14 cups of​ coffee, using 204 ounces of​ coffee, while collecting a total of ​$16.70. How many cups of each size did Kyle​ fill? Kyle filled ___ ​10-oz cup(s), ___ 14-oz cup(s), and ___ ​20-oz cup(s).

Step-by-step explanation:

Lets assume that Kyle fill "a" 10-oz cups of coffee, "b" 14-oz cups of coffee and "c" 20 oz cups of coffee.

a + b + c = 16     (1)

10*a + 14*b + 20*c = 224       (2)

0.95*a + 1.15*b + 1.50*c = 18.60    (3)

Now, multiplying equation (1) by 10 and subtracting it from equation (2), we get

4b + 10c = 64  (4)

Again, multiplying equation (1) by 0.95 and substracting it from equation (3), we get,

0.2b + 0.55c = 3.4    (5)

Now,

Multiplying equation (5) by 20 and subtracting it from equation (4), we get

-c = -4,

Hence, c= 4

Putting this value in equation (4),

4b + 40 = 64

Hence, 4b = 24

So, b = 6

Again, putting the values of b and c in equation (1),

a + 6 + 4 = 16

Thus,

a = 6

Hence, the solution is

a = 6, 10oz cups of coffee

b = 6, 14 oz cups of coffee

c = 4, 20 oz cups of coffee

answer: 4 (:

step-by-step explanation: