Milk and cream are combined to make a 60-liter mixture that is 50 percent butterfat. If the milk is 5 percent butterfat and the cream is 75 percent butterfat, approximately how many liters of milk are in the mixture?

A. 20.00
B. 21.43
C. 30.00
D. 38.57
E. 42.75

PS20433

Looks like a perfect opportunity to use weighted averages
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let x = the number of liters of MILK needed in the mixture
So, the PROPORTION of milk in the mixture = x/60 [since we have a total of 60 liters in the final mixture]

Since we have a total of 60 liters in the mixture, 60 - x = the number of liters of CREAM needed in the mixture
So, the PROPORTION of milk in the mixture = (60 - x)/60
We want the resulting mixture to contain 50% butterfat

Plug all of these values into the equation to get: 50 = (x/60)(5) + ((60 - x)/60)(75)
Multiply both sides by 60 to get: 3000 = (5)(x) + (60 - x)(75)
Expand: 3000 = 5x + 4500 - 75x
Simplify: 3000 = 4500 - 70x
Subtract 4500 from both sides: -1500 = -70x
Solve: x = (-1500)/(-70) = (1500)/(70) = 150/7

If you'd rather not divide 150 by 7, you can quickly evaluate this by first recognizing that 140/7 = 20
So, 150/7 must be a little bit bigger than 20

Answer: B

1. Thanks for catching that. Yes, it should be cream. I have edited my response accordingly.

2. I'm not sure where the 30 comes in.
You can think of this as combining two groups: Milk and Cream.
Each group has a certain percentage of butterfat. Milk is 5% butterfat, and cream is 75% butterfat,
We want the combined mixture to contain 60 liters, and we want that mixture to be 50% butterfat (that's where I got the 50 from)

Does that help?