Joe's Dairy Farm has 100 gallons of milk that is 4.6 percent butterfat How much skim milk should be mixed with it to make milk that is 3.2 percent fat?

let express percentages as fractions so that 1.5%=1.5/100

let express all volumes in gallons so that 50g:= 50

let x be the unknown amount of cream

You can state a linear equation for the absolute fat content as

50 (1.5/100)+x(40/100)=(50+x)(4/100)

Which gives

x(40/100-4/100)=200/100-75/100

multiply both sides by 100

x(40-4)=200-75

divide by 36

x=(200-75)/36=3.48

Thus you have to add 3.48 gallons of cream 40% to 50 gallons of low fat milk 1.5 to have a mixture with 4% fat in it. I hardly expect you can call the mixture "milk" since such a procedure is illegal in most countries.

D.