Arandom sample of 50 dogs at an animal shelter were tested for heart worms , and 4 tested positive. it costs $300 to treat a dog for heart worms. estimate the yearly cost to treat all dogs at the shelter that test positive for heart worms, given that the shelter houses cost about 5750 dogs per year. explain your reasoning

The yearly cost would be $138,000.

We will assume that this sample is typical of the shelter's usual numbers.  We set up a proportion to estimate how many dogs yearly will have heart worm:

4/50 = x/5750

Cross multiply:
50*x = 4*5750
50x = 23000

Divide both sides by 50:
50x/50 = 23000/50
x = 460

We would expect 460 dogs per year to have heart worm.  Multiplying this by the cost for each dog to be treated, we have

460*300 = 138,000.