Question

Stuck with a current word problem

Find how many quarts of 5% butterfat milk and 1% butterfat milk should be mixed to yield 100 quarts of 3% butterfat milk

Answer 1

50 quarts of 5% butterfat and 1% butterfat milk are to be mixed.

SOLUTION:

First, I will set up my table. I will fill in the unknowns with variables x and y.

The table is attached below

From the table attached below, we can easily set up the two equations.

Sum of values of two milks = Value of mixture

0.05x + 0.01y = 3

For convenience, we'll multiply the entire equation by 100,

5 x + y = 300 ------> (1)

Now, Sum of amounts of each acid = Amount of mixture

x + y = 100 ---------> (2)

Subtracting equation (2) from (1),

( + ) 5 x + y = 300

( − ) x - y = 100

− − − − − − − −

( = ) 4x + 0y = 200

Thus, 4x = 200

x = 50

Substituting x = 50 in (2),

( 50 ) + y = 100

y = 100 – 50 = 50

hence, 50 quarts of 5% butterfat and 1% butterfat milk are to be mixed.