Question

This question has two parts. First, answer Part A. Then, answer Part B.

Part A:

Jasmine started a dog walking business in her community. She offers a basic walk service and a deluxe service that includes a trip to the dog park. The expressions in the table represent the number of each type of service she sold over a period of w weeks.

Service Cost ($) Number Sold
Basic Walk 3 7(w + 3)
Deluxe Walk 8 3w + 5

Write an expression that represents the difference between the number of basic walks and deluxe walks sold. Write your answer in factored form.

Answer 1

The difference between the number of basic walks and deluxe walks sold can be represented by the expression 4w + 16.

Step-by-step explanation:

To find the difference between the number of basic walks and deluxe walks sold, we need to subtract the number of deluxe walks from the number of basic walks.

The expression representing the number of basic walks sold is 7(w + 3).

The expression representing the number of deluxe walks sold is 3w + 5.

Therefore, the difference between the number of basic walks and deluxe walks sold can be written as:

7(w + 3) - (3w + 5)

We can further simplify this expression by distributing and combining like terms:

7w + 21 - 3w - 5

Simplifying further, we have:

4w + 16

So, the expression in factored form that represents the difference between the number of basic walks and deluxe walks sold is 4w + 16.