Question

1. a small business sells customer gift baskets. the profit, p, in dollars, is modeled with the given equation p = 40x - (200 + 5x)

their profit is the difference in the amount of money earned selling the gift baskets and the cost of making the gift baskets.
part a: which expression represents the cost of making x gift baskets?
a) 200
b) 40x
c) 200 + 5x
d) 35x - 200
part b: the selling price per gift basket is $

Explanation:

Part A

Step1: Recall Profit Formula

Profit \( P \) is revenue minus cost, so \( P = \text{Revenue} - \text{Cost} \).
Given \( P = 40x - (200 + 5x) \), compare with \( P = \text{Revenue} - \text{Cost} \).

Step2: Identify Cost Expression

Here, \( 40x \) is revenue (money earned from selling \( x \) baskets), and \( (200 + 5x) \) must be the cost (money spent to make \( x \) baskets). So the cost expression is \( 200 + 5x \), which is option c.

Step1: Analyze Revenue Component

Revenue from selling \( x \) baskets is \( 40x \). Revenue is also calculated as (selling price per basket) \( \times \) (number of baskets, \( x \)).

Step2: Find Selling Price

If Revenue \( = \text{Selling Price per basket} \times x = 40x \), then dividing both sides by \( x \) (for \( x
eq 0 \)) gives selling price per basket \( = \frac{40x}{x} = 40 \).

Answer:

c) \( 200 + 5x \)

Part B