SOLUTION: a farmer has cream which is 20% butterfat and some which is 15% butterfat.how many gallons of each must be mixed to produce 50 gallons of cream which is 18% butterfat?

Question 275247: a farmer has cream which is 20% butterfat and some which is 15% butterfat.how many gallons of each must be mixed to produce 50 gallons of cream which is 18% butterfat?
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
a farmer has cream which is 20% butterfat and some which is 15% butterfat.how many gallons of each must be mixed to produce 50 gallons of cream which is 18% butterfat?
Let x be the number of gallons of 20% needed and y the number of gallons of 15% needed. We have then that:
1.) x + y = 50 and
2.) .2*x + .15*y = .18*50
From 1.) we have x = 50 - y. Substituting 50-y for x in 2.) we have:
.2*(50-y) + .15*y = 9
10 - .2*y + .15*y = 9
-.05*y = -1
y = 20
x = (50-y) = (50-20) = 30

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