Reba works at a starbucks coffee shop where a 120z cup of coffee costs $1.65, a 160z cup costs $1.85, and a 20oz cup cost $1.95. During one busy period, Reba served 55 cups of coffee, emptying six 1440z brewers while collecting a total of $99.65. How many cups of each size did reba fill?

Cups of 120oz sold = 17

Cups of 160oz sold = 25

Cups of 200oz sold = 13

Step-by-step explanation:

We know that:

a 120z cup of coffee costs $1.65

a 160z cup costs $1.85

a 200oz cup cost $1.95

Let's define the variables:

A = # of 120z cups that she sold

B = # of 160oz cups that she sold

C  = # of 200oz cups that she sold.

We know that:

"Reba served 55 cups of coffee"

A + B + C = 55.

"emptying six 1440z brewers while"

A*120oz + B*160oz + C*200oz = 6*1440oz

"collecting a total of $99.65"

A*$1.65 + B*$1.85 + C*$1.95 = $99.65

Then we have a system of equations:

A + B + C = 55

A*120oz + B*160oz + C*200oz = 6*1440oz

A*$1.65 + B*$1.85 + C*$1.95 = $99.65

To solve this, the first step is to isolate one of the variables in one of the equations, let's isolate A in the first one:

A = 55 - B - C

Now we can replace that into the other two equations:

(55 - B - C)*120oz + B*160oz + C*200oz = 6*1440oz

(55 - B - C)*$1.65 + B*$1.85 + C*$1.95 = $99.65

Now we can rewrite those equations as:

B*40oz + C*80oz = 8640oz - 55*120oz  = 2040oz

B*$0.20 + C*$0.30 = $99.65 - 55*$1.65 = $8.90

Now we have the system:

B*40oz + C*80oz = 2040oz

B*$0.20 + C*$0.30 = $8.90

Now we need to isolate another variable in one of the equations, let's isolate B in the first one:

B = 2040oz/40oz - C*80oz/40oz = 51 - 2*C

Now we can replace this in the other equation and get:

(51 - 2*C)*$0.20 + C*$0.30 = $8.90

Bow we can solve this for C.

$10.20 - C*$0.40 + C*$0.30 = $8.90

$10.20 - $8.90 = C*$0.10

$1.30 = C*$0.10

($1.30/$0.10) = C = 13

Now we can replace this in the equation:

B = 51 - 2*C = 51 - 2*13 = 25

And for A, we had:

A = 55 - B - C = 55 - 25 - 13 = 17

Then:

Cups of 120oz sold = 17

Cups of 160oz sold = 25

Cups of 200oz sold = 13