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 29 cups of coffee, using 414 ounces of coffee, while collecting a total of $34.05. how many cups of each size did kyle fill?

10Oz = 7 , 14Oz = 16, 20 OZ = 6

Step-by-step explanation:

There three equations that can be made here based on given data

Let number of 10 Oz cup be  x

Let number of 14 Oz cup be y

Let number of 20 Oz cube be z

we can see that

x+y+z=29    (i)

.95x + 1.15y + 1.5z = 34.05   (ii)

10x+ 14y + 20z = 414 (iiI)

We can solve these equations together to get the value of x and y and z  (Done through calculator 3 variable equation function)

x= 7

y=16

z=6

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3