world problem

Question

Find how many quarts of 6% butterfat milk and 3% butterfat milk should be mixed to yield 90 quarts of 4% butterfat milk

Answer 1

For this problem, it's often helpful to make a table. We'll call the number of quarts of 6% milk x, so that the number of quarts of 3% milk must be 90 - x (since we want 90 quarts total). The first row of the table will represent the 6% milk, the second row will represent the 3% milk, and the third row will represent the 4% milk:

 

QUARTS OF MILK         CONCENTRATION OF FAT        QUARTS OF FAT

x                                           0.06                                         0.06(x)

90 - x                                   0.03                                         0.03(90 - x)

90                                         0.04                                         0.04(90)

 

 

Then, since we're mixing the first two rows to make the third row, the following equation should be true. Solve for x:

 

0.06x + 0.03(90 - x) = 0.04(90)

0.06x + 2.7 - 0.03x = 3.6

0.03x + 2.7 = 3.6

0.03x = 0.9

x = 30

 

 

That means we need x = 30 quarts of 6% butterfat milk and 90 - 30 = 60 quarts of 3% butterfat milk.