SOLUTION: an office has two copiers. One makes 8 copies per minute and the other makes 10 copies per minute. If both are used at the same time to make a total of 675 copies, how many copies

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Question 370891: an office has two copiers. One makes 8 copies per minute and the other makes 10 copies per minute. If both are used at the same time to make a total of 675 copies, how many copies are made by each machine? I have the answers but I need to come up with an equation and don't know how to do that. Here are my answers: 300 copies and 375 copies.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=number of minutes required for both machines to make 675 copies
Then 8x+10x=675
18x=675
x=37.5 min time that each machine worked in making 675 copies
Soooo
8*37.5=300 copies for machine that makes 8 copies/min
and
10*37.5=375 copies for machine that makes 10 copies/min
ANOTHER WAY------
Let x=# copies made by first machine (8 copies/min)
And let y=# copies made by second machine (10 copies/min)
Soooo
x+y=675---eq1
and
x=(8/10)y-----eq2
substitute (8/10)y for x in eq1
(8/10)y+y=675
(18/10)y=675
18y=6750
y=375-----# copies made by 2nd machine
from eq1
x+375=675
x=675-375
x=300 # copies made by 1st machine
Hope this helps---ptaylor