SOLUTION: how much lowfat milk (1%) fat and how much whole milk (4% fat) should be mmixed to make 5 gallon of reduced fat milk (2%)

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Question 465029: how much lowfat milk (1%) fat and how much whole milk (4% fat) should be mmixed to make 5 gallon of reduced fat milk (2%)
Found 2 solutions by josmiceli, robertb:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = gallons of 1% milk needed
Let b = gallons of 4% milk needed
given:
(1)+a+%2B+b+=+5+
(2) +%28.01a+%2B+.04b%29+%2F+5+=+.02+
--------------------------
(2) +.01a+%2B+.04b+=+.1+
(2) +a+%2B+4b+=+10+
and, from (1),
(1) +a+=+5+-+b+
By substitution,
(2) +5+-+b+%2B+4b+=+10+
(2) +3b+=+5+
(2) +b+=+5%2F3+
and
(1) +a+%2B+b+=+5+
(1) +a+=+5+-+5%2F3+
(1) +a+=+10%2F3+
10/3 gallons of 1% milk are needed
5/3 gallons of 4% milk are needed
check:
(2) +.01a+%2B+.04b+=+.1+
(2) +.01%2A%2810%2F3%29+%2B+.04%2A%285%2F3%29+=+.1+
(2) +.1%2F3+%2B+.2%2F3+=+.1+
(2) +.1+%2B+.2+=+.3+
(2) +.3+=+.3+
OK

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
0.01x + 0.04(5 - x) = 0.02*5
<==> 0.01x + 0.2 - 0.04x = 0.1
<==> -0.03x = -0.1
<==> x = 10/3 gallons of 1%, and
5 - x = 5/3 gallons of 4%.