multi-step problem

problem: Seminole Dairy Farm has 100 gal of milk that is 4.6% butterfat. How much skim milk (no butterfat) should be mixed with it to make milk that is 3.2% fat?

a: make a table.
b: let x be the amount of skim milk. Complete the columns that show the amount and the percent of butterfat.
c: to find the amount of butterfat in a solution, what two quantities must be multiplied?
d: write expressions that show the amount of butterfat in each solution.
e: Write and solve an equation to answer the problem.

please help me with all these steps. i'm in need of some BIG help.

Well if you wanted to half the percentage of butterfat then you'd add 100 gallons of skimmed milk, i.e. the amounts would be a 1:1 ratio.

The ratio gives the percentage that you want to keep and the percentage you want to remove.

As you want to keep 16 23rds of the butterfat (3.2/4.6), you have a 16:7 ratio of the amounts that need to be used.

So if 100 gallons is 16/23, then 7/23 is...

(7/23) / (16/23) * 100 = 7/23 * 23/16 * 100 = 7/23 * 2300/16 = 16100/368 = 43.75 gallons of skimmed milk should be added

Does this help your table at all?

thank you. it helps a lot.