Question 1165119
<br>
A standard formal algebraic setup for solving the problem....<br>
x = gallons of 1% butterfat
244-x = gallons of 9% butterfat<br>
The mixture of 244 gallons is to be 7% butterfat:<br>
{{{.01(x)+.09(244-x) = .07(244)}}}<br>
That equation is solved using basic algebra, but the numbers are not "nice", so it requires a lot of work.  (I leave it to you to finish solving by that method.)<br>
Here is a quick and easy way to solve a 2-part mixture problem like this with some simple mental arithmetic.<br>
The target percentage, 7%, is 3/4 of the way from 1% to 9%.  (Picture the three percentages on a number line, if it helps....)<br>
That means 3/4 of the total 244 gallons needs to be the 9% butterfat.<br>
ANSWER: 1/4 of 244 gallons, or 61 gallons, of 1% butterfat milk, the other 183 gallons of 9% butterfat milk.<br>
CHECK:
.01(61)+.09(183) = 0.61+16.47 = 17.08
.07(244) = 17.08<br>