how do you set this up

Question

A milk company keeps two kinds of milk on hand, skim milk that has 0.5 %
butterfat and whole milk that contains 4.5 %
butterfat. How many gallons of each type of milk does the company need to produce 320 gal of 1 %
milk for a grocery store?

Answer 1

Hi Tatiana, to solve this type of problem, set up a table with three rows and four columns. Here is what it would look like:

 

Percent      Number     Multiplier         Totals

Milk           of gals

-------------------------------------------------------

0.5%            x              .005         .005 * x

 

4.5%         320 - x        .045         .045(320 - x)

 

1%             320            .01          .01 * 320

 

x, represents the number of gallons of 0.5% skim milk we want to find.

 

The totals column can be represented in an equation: 

 

.005 * x + .045 * (320 - x) = .01 * 320

 

Solve the equation:

 

I do not like to work with decimals, so multiply the entire equation by 1000:

 

5x + 45 * 320 - 45x = 10 * 320

 

14400 - 40x = 3200

 

Subtract 40x from both sides:

 

14400 = 3200 + 40x

 

Subtract 3200 from both sides:

 

14400 - 3200 = 40x

 

11200 = 40x

 

Divide both sides by 40:

 

x = 280

 

Solution:

 

The milk company needs 280 gallons of skim milk and 320 - 280, or 40 gallons of whole milk to make the 320 gallons of 15 milk.

 

Questions?