Question 34579: This exercise is solving applied problems: three equations.
Sally works at Starbucks a 10-oz cup of coffee costs $1.09, a 14-oz cup costs $1.29 and a 20-oz cup costs $1.49. During a busy period, Sally served 34 cups of coffee, emptying five 96-oz pots while collecting $43.46. How many cups of each size did Sally fill?
I know the answer is 8 10-oz, 20 14-oz, and 6 20-oz but how do you get those answers?
Answer by Paul(988)   (Show Source):
You can put this solution on YOUR website! Let the 10-oz cup be x
Let the 14-oz cup be y
Let the 20-oz cup be z
Now we know that:
x+y+z=34 (equation 1)
"emptying five 96-oz pots..." translate that into 5 of 96-oz pots
so
10x+14y+20z=5(96) (equation 2)
109x+129y+149z=4346 (equation 3)
Mutliply equation 1 by 14:
and subbtract 2 by 1:
10x+14y+20z=480
14x+14y+14z=476
-4x+6z=4 (equation 4)
Subbtract equation 2 by equation 3
And mutliply equation 2 by 129 and equation 3 by 14
1290x+1806y+2580z=61920
1526x+1806y+2086z=60844
-236x+494z=1076 (equation 5)
Multiply equation 4 by 236 and subbstract E5 by E4
-236x+494z=1076
-236x+354z=236
140z=840
z=6
-4x+6(6)=4
-4x=-32
x=8
In x+y+z=34
8+y+6=34
y=20
Hence, their are 8 10-oz cups, 20 14-oz cups and 6 20-oz cups.
Paul.
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