SOLUTION: Farmers in many province mill rice using a machine. One farmer use 3 machines A, B and C. When all three machines are working, 114 sacks can be milled in 1 week, when only A and B

Algebra ->  Matrices-and-determiminant -> SOLUTION: Farmers in many province mill rice using a machine. One farmer use 3 machines A, B and C. When all three machines are working, 114 sacks can be milled in 1 week, when only A and B       Log On


   

Question 1005930: Farmers in many province mill rice using a machine. One farmer use 3 machines A, B and C. When all three machines are working, 114 sacks can be milled in 1 week, when only A and B are working, 68 sacks of rice can be milled. When only B and C are working, 84 sacks can be milled in 1 week. How many sacks can produce in 1 week by each machine? Will the number of sacks milled per week
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Unit for rate is SACKS per WEEK. Call their capital letters their corresponding rates.
Any combination of machines working at the same time is the sum of their rates.
system%28A%2BB%2BC=114%2CA%2BB=68%2CB%2BC=84%29

Solve the system any way you want or need.

Here is a possible way.
A=114-B-C
-
system%28%28114-B-C%29%2BB=68%2CB%2BC=84%29
114-B-C%2BB=68
114-C=68
114-68=C
highlight%28C=46%29

B%2BC=84
B=84-C
B=84-46
highlight%28B=38%29

You can find A from those values.
highlight%28A=30%29