SOLUTION: A dairy needs 246 gallons of milk containing 5% butterfat. How many gallons each of milk containing 6% butterfat and milk containing 3% butterfat must be used to obtain the desired

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Question 621625: A dairy needs 246 gallons of milk containing 5% butterfat. How many gallons each of milk containing 6% butterfat and milk containing 3% butterfat must be used to obtain the desired 246 gallons?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=number of gal of 6% butterfat needed
Then 246-x=number of gal of 3% butterfat needed
Now we know that the amount of pure butterfat in the 6% mixture (0.06x) plus the amount of pure butterfat in the 3% mixture(0.03(246-x)) has to equal the amount of pure butterfat in the final mixture(0.05*246), soooooo:
0.06x+0.03(246-x)=0.05*246 simplify
0.06x+7.38-0.03x=12.3
0.03x=12.3-7.38
0.03x=4.92
x=164 gal------amount of 6% butterfat needed
246-164=82----amount of 3% butterfat needed
CK
164*0.06+82*0.03=0.05*246
9.84+2.46=12.3
12.3=12.3
Hope this helps---ptaylor