228k views
3 votes
how many gallons of each milk containing 7% buttermilk and milk containing 2% butterfat must be used to obtain 375 gallons?

how many gallons of each milk containing 7% buttermilk and milk containing 2% butterfat-example-1
User SirPilan
by
4.4k points

1 Answer

3 votes

Let:

x = Gallons of milk 7% fat

y = Gallons of milk 2% fat

The total gallons of milk needed is 375, thus:

x + y = 375 [Equation 1]

x gallons of milk add 0.07x fat to the mix and y gallons of milk add 0.02 fat to the mix. The total fat of the mix is:

0.07x + 0.02y

We know the total fat must be 5% of 375 gallons, that is:

0.05 x 575 = 18.75

Therefore, we get the equation:

0.07x + 0.02y = 18.75 [Equation 2]

Solving equaton 1 for x:

x = 375 - y

Substituting in equation 2:

0.07(375 - y) + 0.02y = 18.75

Operating:

26.25 - 0.07y + 0.02y = 18.75

Subtracting 26.25:

- 0.07y + 0.02y = 18.75 - 26.25

Operating:

-0.05y = -7.5

Dividing by -0.05:

y = 150

Calculating x = 375 - y

x = 375 - 150 = 225

Solution:

225 gallons of milk containing 7% butterfat

150 gallons of milk containing 2% butterfat

User Daniel Neal
by
4.3k points