SOLUTION: FIND HOW MANY QUARTS OF 6% BUTTERFAT MILK AND 2% BUTTERFAT MILK SHOULD BE MIXED TOGETHER TO YEILD 80 QUARTS OF 5% BUTTERFAT MILK? please help asap

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Question 230945: FIND HOW MANY QUARTS OF 6% BUTTERFAT MILK AND 2% BUTTERFAT MILK SHOULD BE MIXED TOGETHER TO YEILD 80 QUARTS OF 5% BUTTERFAT MILK? please help asap
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = quarts of 6% butterfat milk needed
Let b = quarts of 2% butterfat milk needed
given:
a+%2B+b+=+80
.06a = butterfat in a
.02b = butterfat in b
In words:
(quarts of butterfat in 5% milk)/(total quarts of 5% milk) = 5%
(1) %28.06a+%2B+.02b%29%2F80+=+.05
(2) +a+%2B+b+=+80
---------------------
Multiply both sides of (1) by 80
(1) .06a+%2B+.02b+=+.05%2A80
(1) .06a+%2B+.02b+=+4
(1) 6a+%2B+2b+=+400
Multiply both sides of (2) by 2 and
subtract from (1)
(1) 6a+%2B+2b+=+400
(2) -2a+-+2b+=+-160
4a+=+240
a+=+60
and
a+%2B+b+=+80
b+=+80+-+60
b+=+20
60 quarts of 6% milk and 20 quarts of 2% milk are needed
check:
(1) %28.06a+%2B+.02b%29%2F80+=+.05
(1) %28.06%2A60+%2B+.02%2A20%29%2F80+=+.05
(1) %283.6+%2B+.4%29%2F80+=+.05
(1) 4%2F80+=+.05
(1) .05+=+.05
OK