A farmer has some cream which is 21 butterfat and some which

A farmer has some cream which is 21% butterfat and some which is 15% butter fat. How many gallons of each must be mixed to produce 60 gallons of cream which is 19% butterfat?

Solution

let the number of gallons of 21% butterfat mixed be x

let the number of gallons of 15% butterfat mixed be y

Given total gallons = 60

==> x + y = 60 ----------- (1)

and 21% butterfat in x gallons ==> butterfat = 0.21x

15% butterfat in y gallons ==> butterfat = 0.15y

mixture\'s butterfat content = 19% = (0.19)(60) = 11.4

==> 0.21x + 0.15y = 11.4 -------------- (2)

solving (1) and (2)

0.21 * (1) - (2) ==> 0.21x + 0.21y - (0.21x + 0.15y) = (0.21)60 - 11.4

==> 0.21x + 0.21y - 0.21x - 0.15y = 1.2

==> 0.06y = 1.2

==> y = 1.2/0.06

==> y = 20

==> x = 60 - 20 = 40

Hence 40 gallons of 21% butterfat cream must be mixed with 15% butterfat cream to produce 60 gallons of 19% butterfat cream.