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 21 cups of​ coffee, using 294 ounces of​ coffee, while collecting a total of ​$24.35. How many cups of each size did Kyle​ fill? Kyle filled ___ 10-oz cup(s), ___ 14-oz cup(s), and ___ ​20-oz cup(s).

kyle works at a donut shop, where a 10oz. cup of coffee costs 95c, a 14 oz. cup of coffee costs $1.15, and a 20oz. cup costs $1.50. during one busy period Kyle served 24 cups of coffee, using 384 ounces of coffee, while collecting a total of $30.60. How many cups of each size did kyle fill.

Let x = no. of 10 oz cups sold

Let y = no. of 14 oz cups sold

Let z = no. of 20 oz cups sold

Equation 1: total number of cups sold:

x + y + z = 24

Equation 2: amt of coffee consumed:

10x + 14y + 20z = 384

Equation 3: total revenue from cups sold

.95x + 1.15y + 1.50z = 30.60

Mult the 1st equation by 20 and subtract the 2nd equation from it:

20x + 20y + 20z = 480

10x + 14y + 20z = 384

subtracting eliminates z

10x + 6y = 96; (eq 4)

Mult the 1st equation by 1.5 and subtract the 3rd equation from it:

1.5x + 1.5y + 1.5z = 36.00

.95x + 1.15y+ 1.5z = 30.60

subtracting eliminates z again

.55x + .35y = 5.40; (eq 5)

Multiply eq 4 by .055 and subtract from eq 5:

.55x + .35y = 5.40

.55x + .33y = 5.28

eliminates x

0x + .02y = .12

y = .12/.02

y = 6 ea 14 oz cups sold

Substitute 6 for y for in eq 4

10x + 6(6) = 96

10x = 96 - 36

x = 60/10

x = 6 ea 10 oz cups

That would leave 12 ea 20 oz cups (24 - 6 - 6 = 12)

Check our solutions in eq 2:

10(6) + 14(6) + 20(12) =

60 + 84 + 240 = 384 oz

answer: need picture of problem

step-by-step explanation:

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.