Find how many quarts 6% butterfat milk and 3% butterfat milk should be mixed to yield 30 quarts of 4% butterfat milk

Question

I merely need to know the x and y values of the equation

Answer 1

6%*x+3%*(30-x)=4%*30 where x=# of pounds of each type-no need for 2 variables although you could use 2 if you like but would have to have 2 equations and then substitute, which basically is already done using 1 variable

0.06x+0.03*(30-x)=0.04*30

0.06x+0.9-0.03x=1.2

0.03x+0.9=1.2

0.03x=1.2-0.9

0.03x=0.3

3x=30

x=30/3

x=10 quarts of the 6% butterfat milk

30-x=30-10=20 quarts of the 3% butterfat milk

 

Answer 2

Here is one way to solve this problem...

 

Lets let A = the quarts of 6% BFM and B = quarts of 3% BFM in our mixture...

 

We know that A+B=30 since we are to make 30 quarts of 4% mixture...

 

We also know that .06A+.03B = the totally amount of Butterfat in our mixture, and this should be a 4% concentration, so

(.06A+.03B)/30 =.04 or equivalently .06A+.03B=1.2 or 2A+B=40...

 

Subtracting the first equation from this equation yield A=10, and we see that we need B=20 to satisfy both equations.

 

 

This means that taking 10quarts of 6% concentrate with 20quarts of 3% concentrate will yield 30quarts with total Butterfat in quarts = (.06*10+.03*20)=1.2, and since 1.2/30 = .04, this mixture has a concentration of 4% Butterfat.

 

Hope that helps!