Task 3
Your parents heard about the success of your business and they want to help you out. Suppose they want to give you an additional $300 to put toward your business.
However, there's a catch. If you make more than $600 total, you have to give them 10% of your earnings above $600. For example, if you have earned $650, then you owe 10% of $50, or $5, to your parents.
a. Now that you have an additional $300, revise your inequality from part A of Task 2 to reflect your new spending limit. Solve this inequality and graph the solution on a number line. Explain what your solution means in terms of the situation.
b. If you still sell your item for the same price, what is the most money you can hope to earn from your business now?
c. Will you have to pay your parents? If so, determine how much you will owe
d. Think about how much time it will take you to create your product. You have 200 hours this summer to devote to creating your product. Write an inequality that represents your time constraint.
e. Solve your inequality from part D and graph your solution on a number line.
Explain what your solution means in terms of the situation.
f. With the costs taken into account, what was your total profit? Did you make or lose money? Now that you have these values, would you adjust your business plan from Task 1? If so, how?
a. The revised inequality is: 3x + 300 ≤ 600. Solving this inequality, we get:
3x ≤ 600 - 300
3x ≤ 300
x ≤ 300/3
x ≤ 100.
The solution to this inequality means that the maximum earnings I can have without having to give 10% to my parents is $100.
b. If I still sell my item for the same price, the most money I can hope to earn from my business now is $100, because any amount above that will require me to give 10% to my parents.
c. No, I won't have to pay my parents since the maximum amount I can earn is $100, which is below the threshold of $600. Hence, I don't owe them any money.
d. The inequality representing my time constraint is: t ≤ 200, where t represents the time in hours.
e. The solution to the inequality from part d is t ≤ 200. Graphing this solution on a number line, we'll have 200 as the endpoint of the line, and any value less than or equal to 200 to the left of it will be within the solution.
f. Since the maximum amount I can earn is $100 and I don't have any expenses mentioned, my total profit will be $100. I neither made nor lost money. Considering these values, I might adjust my business plan from Task 1 to explore methods to increase my earnings or reduce expenses in order to make a profit.