Question

A dairy needs296 gallons of milk containing6% butterfat. How many gallons each of milk containing9% butterfat and milk containing1% butterfat must be used to obtain the desired296 gallons?

Answer 1

Let x = gallons of 9% butterfat and milk needed

y = gallons of 1% butterfat and milk needed

Now, the total needed gallons are 296. Therefore,

x + y = 296. (i)

Also, it says that the sum of gallons containng 9% milk and 1% milk should be equal to the amount of butterfat produced by 296 gallons of 6% butter fat.

So,

gallons of butterfat in 9% = 0.9x

gallons of butterfat in 1% = 0.1y

total amount with 6% butterfat in 296 gallons = 0.6* 296 = 177.6

so, the equation is

0.9x + 0.1y = 177.6

Multiplying both sides by 10, we get

9x + y = 1776 (ii)

Now, subtract equation (i) from equation (ii).

(9x + y) - (x + y) = 1776 - 296

8x = 1480

x = 185

Put the values of x in equation (i), we can get the value of y

185 + y = 296

y = 296 - 185

y = 111

Therefore, you need 185 gallons of 9% butterfat milk and 111 gallons of 1% butterfat milk.