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.
