Algebra 1 A

I am a little unsure of how to answer this question:

Write an inequality to represent the limit you may not exceed when spending to make your product.

Here's the background information I have.

You are going to decide on a summer business to start. Figure out what you will do, how much it will cost you, and how much you will charge.

Total amount of money you will be investing:

What item are you making and selling and also why?
The item I'm making is fresh squeezed lemonade because it's a profitable business in the summer and I like lemonade.

Describe the setup of your business:
Cost to make each item: $0.20 per cup and $2.33 per gallon
Selling price of each item: $0.50 per cup

Please help me as soon as you can. Thank you!

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  1. money <= 100
    cost for x gallons (16 cups/gal)
    = .20*16x + 2.33x
    = 5.53x

    sales: .50*16x = 8.00x

    profit: 2.47x

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  2. Okay using Cassidy s example how would I solve the following questions. I just need to understand the concept using her problem.
    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 them.
    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?

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