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

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.

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it