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
Accepted Solution
A:
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 belowFrom 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 = 50Substituting 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.