SOLUTION: The number of cows on a farm increased by 60. Because of better food, the amount of milk from each cow went up from 12.8 liters per day to 15 liters per day on the average. How man

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The number of cows on a farm increased by 60. Because of better food, the amount of milk from each cow went up from 12.8 liters per day to 15 liters per day on the average. How man      Log On


   

Question 1013612: The number of cows on a farm increased by 60. Because of better food, the amount of milk from each cow went up from 12.8 liters per day to 15 liters per day on the average. How many cows are on the farm if the farmer gets 1340 liters of milk more per day?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of cows originally
on the farm
+12.8n+ = liters of milk from +n+ cows
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+n+%2B+60+ = number of cows later on
+15%2A%28+n+%2B+60+%29+ = liters of milk from +n+%2B+60+ cows
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Let +m+ = liters of milk/day originally
+m+%2B+1340+ = liters of milk later on
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Equation for case with +n+ cows:
(1) +m+=+12.8n+
Equation for case with +n+%2B+60+ cows
(2) +m+%2B+1340+=+15%2A%28+n+%2B+60+%29+
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Substitute (1) into (2)
(2) +12.8n+%2B+1340+=+15%2A%28+n+%2B+60+%29+
(2) +12.8n+%2B+1340+=+15n+%2B+900+
(2) +15n+-+12.8n+=+1340+-+900+
(2) +2.2n+=+440+
(2) +n+=+200+
and
+n+%2B+60+=+260+
There are 260 cows on the farm
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check:
(1) +m+=+12.8n+
(1) +m+=+12.8%2A200+
(1) +m+=+2560+
and
(2) +m+%2B+1340+=+15%2A%28+n+%2B+60+%29+
(2) +m+%2B+1340+=+15%2A%28+200+%2B+60+%29+
(2) +m+%2B+1340+=+3900+
(2) +m+=+2560+
OK