Tim and Judy mix twq kinds of feed for pedigreed dogs. They wish to make 25 pounds of feed worth .27 per pound by mixing one kind worth .19 per pound with another worth .53 per pound. How many pounds of the cheaper kind should they use in the mix? Round your answer to the nearest pound, if necessary.

They want to mix .19 per pound of one type + .53 per pound of another type and get .27 per pound of both. So:

.19x + .53y = .27(x+y), where x and y are the amounts of each type of dog food

Then, .19x + .53y = .27x + .27y

.26y = .08x, and x/y = .26/.08, so x/y = 3.25, and y = x/3.25

You also know that when you add each amount together you have to get 25 pounds, so x+y = 25

Now, sub in for y:

x + (x/3.25) = 25, and 3.25x + x = 25(3.25), so 4.25x = 81.25, and x=19.12. So they want to use 19.12 pounds of the cheap kind and (25-19.12) 5.88 pounds of the other kind. Sub in x and y into the original equation to check your answer. You will get 6.25 on both sides.