Question

a dairy needs 306 gallon of milk containing 6% butterfat. how much gallons each of milk containing 7% butterfat and milk containing 4% butterfat must be used to obtain the desired 306 gallons?

Answer 1

$306 \times 6\%=306 \times 0.06=18.36$
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

$x+y=306 \\ 7\%x + 4\%y=18.36 \\ \\ x+y=306 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\times (-4) \\ 0.07x+0.04y=18.36 \ \ \ \ |\times 100 \\ \\ -4x-4y=-1224 \\ \underline{7x+4y=1836 \ \ \ \ \ \ } \\ 7x-4x=1836-1224 \\ 3x=612 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 3 \\ x=204 \\ \\ x+y=306 \\ 204+y=306 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |-204 \\ y=102$

204 gallons of 7% milk and 102 gallons of 4% milk should be used.