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Question 1142546: hello i have been working on this question for a while but I keep getting so confuse with what i have been writing on my piece of paper.
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 31 cups of coffee, using 484 ounces of coffee, while collecting a total of $38.80. How many cups of each size did Kyle fill?
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441)   (Show Source):
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! 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 31 cups of coffee, using 484 ounces of coffee, while collecting a total of $38.80.
How many cups of each size did Kyle fill?
:
let a = no. of 10 oz cups
let b = no. of 14 oz cups
let c = no. of 20 oz cups
:
You can use the matrix feature on you calc to solve this
1 1 1 31
10 14 20 484
.95 1.15 1.5 38.8
:
A more tedious method using elimination
write an equation for each statement
a + b + c = 31
10a + 14b + 20c = 484 oz
.95a + 1.15b + 1.50c = $38.80
:
multiply the 1st equation by 10, subtract from the 2nd equation
10a + 14b + 20c = 484
10a + 10b + 10c = 310
-------------------------eliminates a, give us a 2 unknown equation
0 + 4b + 10c = 174
then
multiply the 1st equation by .95, subtract from the 3rd equation
.95a + 1.15b + 1.50c = 38.80
.95a + .95b + .95c = 29.45
-----------------------------eliminates a, another 2 unknown equation
0 + .2b + .55c = 9.35
multiply by 20, subtract the 1st 2 unknown eq
4b + 11c = 187
4b + 10c = 174
-----------------subtraction eliminates b, find c
0 + c = 13 ea 20 oz cups
then
4b + 11(13) = 187
4b + 143 = 187 - 143
4b = 187 - 143
4b = 44
b = 44/4
b = 11 ea 14 oz cups
then
a + 11 + 13 = 31, you can find the 10 oz cups
:
I check my solutions using the matrix feature on my Ti83
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