A bookstore owner has monthly fixed costs of $5,500, and for each book sold, she has additional costs of $0.40. The owner does not want her average monthly costs to exceed $7,000. If b is the average number of books sold per month, which of the following inequalities best represents this situation? Choose 1 answer: (A) 5,500+0.40 b 7,000 (B) 0.40(5,500+b)

Question

A bookstore owner has monthly fixed costs of  $5,500, and for each book sold, she has additional costs of  $0.40. The owner does not want her average monthly costs to exceed  $7,000. If  b is the average number of books sold per month, which of the following inequalities best represents this situation? Choose 1 answer: (A)  5,500+0.40 b > 7,000 (B)  0.40(5,500+b) <= 7,000 (C)  5,500+40 b <= 7,000 (D)  5,500+0.40 b <= 7,000

Bytelearn · Accepted Answer

Fixed Monthly Costs: The bookstore owner has fixed monthly costs of $5,500. This is a constant value that does not change with the number of books sold. Variable Costs for Books: For each book sold, there is an additional cost of $0.40. If b represents the average number of books sold per month, then the total variable cost for books is 0.40b. Total Monthly Cost: The total monthly cost is the sum of the fixed costs and the variable costs. Therefore, the total monthly cost can be represented by the expression 5,500 + 0.40b. Target Monthly Cost: The owner wants the average monthly costs to stay below $7,000. This means the total monthly cost must be less than or equal to $7,000. Inequality Representation: Combining the information from the previous steps, we can write the inequality that represents the situation as 5,500 + 0.40b <= 7,000. Matching Answer Choice: Now we need to check the answer choices to see which one matches our inequality. Choice (D) is 5,500 + 0.40b <= 7,000, which is exactly what we derived.

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