Word problem...system of equations...BEST answer to first right one

A man works at a factory where 10oz cups of drink cost .95
a 14oz drink costs 1.15
and a 20 oz drink costs 1.50

He served 29 cups of drink using 394 oz of drink
while collecting a total of 33.05

How many cups of each size did he fill?

10oz=___cups
14oz=___cups
20oz=___cups

THANKS SO MUCH

First write it out as a set of formulas;
394 oz = A x 10 oz + B x 14 oz + C x 20 oz
$ 33.05 = A x $ 0.95 + B x $ 1.15 + C x $ 1.50
29 cups = A + B + C

Sort for one of the variables;
A = 29 - B - C
A = (33.05 - B x 1.15 - C x 1.50) : 0.95
A = (394 - B x 14 - C x 20) : 10

(394 - B x 14 - C x 20) : 10 = 29 - B - C
39.4 - B x 1.4 - C x 2 = 29 - B - C
39.4 - 29 = 1.4 B - B + 2 C - C
10.4 = 0.4 B + C

(33.05 - B x 1.15 - C x 1.50) : 0.95 = 29 - B - C
33.05 - B x 1.15 - C x 1.50 = (29 - B - C) x 0.95
33.05 - 27.55 = 1.15 B - 0.95 B + 1.5 C - 0.95 C
5.5 = 0.2 B + 0.55 C

10.4 = 0.4 B + C and 5.5 = 0.2 B + 0.55 C or rather 11 = 0.4 B + 1.1 C
0.4 B = 10.4 - C and 0.4 B = 11 - 1.1 C
10.4 - C = 11 - 1.1 C
1.1 C - C = 11 - 10.4
0.1 C = 0.6
C = 6 (finally!!!)

0.4 B = 10.4 - C
B = (10.4 - 6) : 0.4 = 11 (nearly there!!)
A = 29 - B - C = 29 - 11 - 6 = 12 (done!)

Variables:

a = number of 10 oz cups
b = " 14 oz cups
c = " 20 oz cups

He served 29 cups, so

a + b + c = 29

he used 394 oz, so

10a + 14b + 20c = 394

and he made 33.05, so

0.95a + 1.15b + 1.5c = 33.05

now solve

x = number of 10oz cups
y = number of 14oz cups
z = number of 20oz cups

10x + 14y + 20z = 394
.95x + 1.15y + 1.50z = 33.05
x + y + z = 29

That should get you started...

10oz=_12__cups
14oz=_11__cups
20oz=__6_cups