[tex]306 \times 6\%=306 \times 0.06=18.36[/tex]
306 gallons of milk containing 6% butterfat contain 18.36 gallons of butterfat.
x - the number of gallons of 7% milk
y - the number of gallons of 4% milk
[tex]x+y=306 \\
7\%x + 4\%y=18.36 \\ \\
x+y=306 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\times (-4) \\
0.07x+0.04y=18.36 \ \ \ \ |\times 100 \\ \\
-4x-4y=-1224 \\
\underline{7x+4y=1836 \ \ \ \ \ \ } \\
7x-4x=1836-1224 \\
3x=612 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 3 \\
x=204 \\ \\
x+y=306 \\
204+y=306 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |-204 \\
y=102[/tex]
204 gallons of 7% milk and 102 gallons of 4% milk should be used.
