Question

Hannah and her band want to record and sell CDs. There will be a set-up fee of $400, and each CD will cost $3.75 to burn. The recording studio requires a minimum order of $1000. What is the minimum number of CDs the band can burn to meet the minimum purchase of $1000? Write an inequality to find the solution.

A) C ≥ 1000 - 400 / 3.75
B) C ≤ 1000 - 400 / 3.75
C) C ≥ 1000 + 400 / 3.75
D) C ≤ 1000 + 400 / 3.75

Answer 1

To find the minimum number of CDs Hannah's band can burn, we subtract the setup fee from the minimum purchase and then divide by the cost per CD. The correct inequality is A) C ≥ (1000 - 400) / 3.75, which calculates the number of CDs needed to satisfy the recording studio's minimum order requirement.

Step-by-step explanation:

To determine the minimum number of CDs Hannah and her band can burn to meet the minimum purchase of $1000, we need to consider the setup fee and the cost per CD. Since there is a setup fee of $400, the remaining budget to burn CDs would be $1000 - $400 = $600. With each CD costing $3.75 to burn, we can set up the following inequality:

Cost to burn CDs + Setup Fee ≥ Minimum Purchase

3.75C + 400 ≥ 1000

To solve for the minimum number of CDs (C), we need to subtract the setup fee from both sides of the inequality:

3.75C ≥ 1000 - 400

3.75C ≥ 600

Now, dividing both sides by the cost per CD will give us the minimum number of CDs required:

C ≥ 600 / 3.75

So the correct inequality that represents the solution is:

A) C ≥ (1000 - 400) / 3.75