Milk and cream are combined to make a 60-liter mixture that is 50 percent butterfat. If the milk is 5 percent

BTGmoderatorDC wrote: ↑

Mon Jul 18, 2022 1:16 am

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


OA B

Source: GMAT Prep

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 cream 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