Question 1142546
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