Question

You decide to start your own business of washing dogs. first, you purchase $50 in supplies (buckets, towels, hoses, etc.). when you buy a 32 oz. bottle of shampoo for $4.79, the label says that it will wash a dog 32 times. using the scenario:

1. find the per-dog cost for the shampoo. describe how you found the amount.
2. determine the cost equation, c(x), for washing dogs. don’t forget that you spent $50 on supplies.
3. your mom offers to pay $3 for your dog to be washed. explain below why you think your mom’s price is reasonable, too little, or too much.

Answer 1

The per-dog cost for the shampoo is $0.1497, and the cost equation for washing dogs is c(x) = 50 + 0.1497x. Whether your mom's offer of $3 is reasonable depends on how it compares to your average costs as you wash more dogs.

Step-by-step explanation:

To find the per-dog cost for the shampoo, divide the total cost of the shampoo ($4.79) by the number of dogs it can wash (32). This gives:

(4.79 dollars) / (32 dogs) = (0.1497 dollars/dog).

For the cost equation c(x) for washing dogs, you include the initial $50 in supplies as fixed costs and then add the per-dog cost of the shampoo for each dog x. Therefore:

c(x) = 50 dollars + (0.1497 dollars/dog) * x

If your mom offers to pay $3 for your dog to be washed, you need to compare this to your average cost per dog, including fixed costs. As you wash more dogs, your average cost per dog will go down, so if you wash enough dogs, $3 might eventually cover your costs and provide a profit. However, if you wash only a few dogs, $3 might not be enough to cover your fixed and variable costs.