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

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: