Question

You’ve decided to start your own business and sell handmade toys. You found an online supplier, Company A, where you pay $11 for each of the toys plus $10 shipping. You will sell the toys for $13 each. Since you are just starting out, you can’t spend more than $150 to get the toys.

1. Write an inequality that represents the fact that you can’t exceed this spending limit.

2. What situation is modeled by the inequality?

3. You decide to purchase 30 toys. Your first few customers each buy 3 toys, and you now have at least 14 toys. Which inequality represents this situation?

Answer 1

1. 11x + 10 ≤ 150

2. Company B charges $12 per toy. Company A charges $11 per toy plus $10 shipping. So, this inequality represents the cost for Company A will be greater.

3. 30 - 3c ≥ 14

Explanation:

1. Company A demands to pay $11 for each of the toys plus $10 shipping charges.

But I can not spend more than $150 to get the toys.

So, the inequality that represents the fact that I can not exceed this spending limit is 11x + 10 ≤ 150. (Answer)

2. Given the inequality 12x < 11x + 10.

The situation is modeled by this inequality is Company B charges $12 per toy. Company A charges $11 per toy plus $10 shipping. So, this inequality represents the cost for Company A will be greater. (Answer)

3. 30 toys that I have to purchase. My first few customers each buy 3 toys and I now have at least 14 toys. The inequality that represents this situation is 30 - 3c ≥ 14 (Answer)