SOLUTION: together, two printers can print 7500 lines if the first printer prints for 2 minutes and the second prints for 1 minute. If the first prints for 1 minute and the second prints for

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Question 210061: together, two printers can print 7500 lines if the first printer prints for 2 minutes and the second prints for 1 minute. If the first prints for 1 minute and the second prints for 2 minute, they can print 9000 lines together. Find the number of lines per minute that each printer prints.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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together, two printers can print 7500 lines if the first printer prints for 2
minutes and the second prints for 1 minute.
If the first prints for 1 minute and the second prints for 2 minute, they can
print 9000 lines together.
Find the number of lines per minute that each printer prints.
:
Let x = printing rate of the 1st printer (lines/min)
Let y = printing rate of the 2nd printer
;
2x + 1y = 7500; (1st printer prints for 2 minutes and the 2nd prints for 1 min.)
1x + 2y = 9000; (1st printer prints for 1 minutes and the 2nd prints for 2 min.)
:
Use the 1st equation for substitution
y = (7500-2x)
:
Substitute (7500-2x) for y in the 2nd equation
1x + 2(7500-2x) = 9000
1x + 15000 - 4x = 9000
1x - 4x = 9000 - 15000
-3x = -6000
x = %28-6000%29%2F%28-3%29
x = +2000 line/min for the 1st printer
;
Find the rate of the 2nd printer
y = (7500 - 2(2000)
y = 7500 - 4000
y = 3500 line/min for the 2nd printer
:
:
Check solution in original 2nd equation:
1x + 2y = 9000
2000 + 2(3500) = 9000;