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.
Now that you have an additional $300, revise your inequality from part A of Task 2 to reflect your new spending limit. Example: Add $300 to the total amount you had to spend $200 + $300 = $500, so .63c ≤ 500.
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Solve this inequality. Explain what your solution means in terms of the situation. Example: .63c ≤ 500, c = 793.65, so I can sell 793 cups of lemonade.
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If you still sell your item for the same price, what is the most money you can hope to earn from your business now? Example: 1.50(793) - .63(793) = $395.87
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Will you have to pay your parents? If so, determine how much you will owe them. Example: 10% of whatever you make over $600. If I made $780, 780-600 = 280. 10% of 280 = $28, so I would owe my parents $28.
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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. Example: if each cup takes me 8 minutes to make, 8c ≤ 12,000 (since I’m working with minutes, I want to turn the 200 hours into minutes. 200 x 60 = 12000 minutes in 200 hours).
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Solve your inequality from part D. Explain what your solution means in terms of the situation. Example: 8c ≤ 12,000, so c ≤ 1500minutes 🡪 c ≤ 25 hours, so I am only using 1/8 of the 200 hours to make my product (to find out how many hours from minutes, divide the number of minutes by 60).
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Revised inequality from part A:
.63c + 300 ≤ 600
Solve this inequality:
.63c + 300 ≤ 600
.63c ≤ 300
c ≤ 476.19
Explanation: The solution to the revised inequality is c ≤ 476.19. This means that with the additional $300, you can spend no more than $476.19 on your business.
If you still sell your item for the same price, the most money you can hope to earn from your business now is:
1.50c - .63c = .87c
.87(476.19) = $414.61
Explanation: The most money you can hope to earn from your business now is $414.61.
You will have to pay your parents if you make more than $600. The amount you will owe them can be calculated by finding 10% of your earnings above $600.
For example, if you made $780:
780 - 600 = 180
10% of 180 = $18
Explanation: If you make $780, you will owe your parents $18.
The inequality that represents your time constraint is:
8c ≤ 12,000
Explanation: The inequality 8c ≤ 12,000 represents your time constraint. It means that the amount of time it takes to create your product, c multiplied by 8, should be less than or equal to 12,000 minutes.
Solve the inequality from part D:
8c ≤ 12,000
c ≤ 1,500
Explanation: The solution to the inequality is c ≤ 1,500. This means that you can complete your product in a maximum of 1,500 minutes or 25 hours, using 1/8 of the 200 hours available this summer (since 1 hour is equal to 60 minutes, divide the number of minutes by 60 to get the number of hours).