Solve for a dairy needs 275 gallons of milk containing 5% butterfat. how many gallons each of milk containing 7% butterfat and milk containing 2% butterfat must be used to obtain the desired 275 gallons?

X = gallons of the 7% butterfat milk

y = gallons of the 2% butterfat milk

now, we'll be adding "x" gallons of the 7% one, but we know that, is really "x" gallons, but only 7% of it is butterfat, the rest is water and other subtances.

so, in "x" gallons, how many gallons is butterfat only anyway?  namely, what is 7% of "x"?  well, (7/100) * x, or 0.07x.

likewise, how many gallons of butterfat are in the 2% one?  well, (2/100) * "y" or 0.02y.

we know that, whatever "x" and "y" add up to 275 gallons, thus x + y = 275.

we also know that, the butterfat amounts add up to the same butterfat in the 275 gallons, thus





how much will it be of the 2% milk?  well, y = 275 - x.