Question 1138730: When both copying machines A and B are working together, secretaries can make 100 copies in one minute. Copiers A and C working together produce 140 copies per minute. When all three copying machines are working together they produce 180 copies per minute. How many copies per minute can each machine produce?
Answer by ikleyn(52802)   (Show Source):
You can put this solution on YOUR website! .
Let "a" be the number of copies the machine A makes per minute,
"b" be the number of copies the machine B makes per minute, and
"c" be the number of copies the machine C makes per minute.
From the condition, we have these equations
a + b = 100 (1)
a + c = 140 (2)
a + b + c = 180 (3)
To solve the system, first subtract equation (1) from equation (3). You will get
c = 180 - 100 = 80.
Next step subtract equation (2) from equation (3). You will get
b = 180 - 140 = 40.
To find "a", substitute b= 40 into equation (1):
a + 40 = 100, which implies a = 100 - 40 = 60.
ANSWER. a= 60; b= 40; c= 80.
Solved.
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The problem also can be solved mentally.
To see many other similar solved problems, look into the lessons
- The tricks to solve some word problems with three and more unknowns using mental math
in this site.
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