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 additional profit, 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.

If you still sell your item for the same price, what is the most money you can hope to earn from your business now?

and will you have to pay your parents?

The most money you can hope to earn from your business now is $600 (the additional amount you received from your parents) plus $600 (the maximum profit limit before owing your parents) which equals $1200.

To determine if you have to pay your parents, you need to calculate your profit above $600:
Profit above $600 = Total earnings - $600

Let's consider different scenarios:

1. If your profit above $600 is less than or equal to $0, you don't have to pay your parents.
2. If your profit above $600 is greater than $0, you owe your parents 10% of the profit above $600.

In this case, you would need to provide the specific amount you have earned above $600 to determine if you owe your parents any money.

To calculate the maximum earnings you can hope to make from your business, you need to consider the additional $300 your parents are giving you and the condition that you have to give them 10% of earnings above $600.

Let's break it down step by step:

1. Start by adding the additional $300 your parents are giving you to your current earnings:
Current earnings + $300

2. Determine the threshold for when you have to start giving your parents a percentage of your earnings:
Threshold = $600

3. Calculate the maximum earnings without having to give your parents any money:
Maximum earnings without paying parents = Threshold + Additional money from parents
= $600 + $300
= $900

So, you can hope to earn a maximum of $900 from your business.

Now, let's see if you have to pay your parents:

4. Calculate the total earnings including the additional $300:
Total earnings = Current earnings + Money from parents
= Current earnings + $300

5. Calculate the additional profit above $600:
Additional profit = Total earnings - Threshold
= (Current earnings + $300) - $600

6. Check if the additional profit is greater than $600:
If Additional profit > $600
then you have to pay your parents the 10% of the excess amount. Otherwise, you don't.

In this specific scenario, you haven't provided the current earnings amount. So, without that information, it is not possible to determine if you would have to pay your parents.

To determine the most money you can hope to earn from your business now and whether you will have to pay your parents, we need to calculate the additional profit you can make with the additional $300 and compare it to the threshold of $600.

To calculate the additional profit, we first need to subtract the initial cost of the business. Let's assume this cost is C dollars.

1. Calculate the maximum profit without the additional $300: P1 = Revenue - Cost

2. Calculate the maximum profit with the additional $300: P2 = (Revenue + $300) - Cost

Now, if P2 is greater than $600, you will owe 10% of the earnings above $600 to your parents. Otherwise, you will not owe them anything.

3. Compare P2 to $600:

a. If P2 ≤ $600, you will not owe anything to your parents, and the most money you can hope to earn from your business is P2.

b. If P2 > $600, calculate the amount you owe to your parents: Owe = 10% * (P2 - $600)

c. Subtract the amount you owe to your parents from the maximum profit: Final Profit = P2 - Owe

Let's go through an example:

1. Calculate maximum profit without the additional $300:
P1 = Revenue - Cost

2. Calculate maximum profit with the additional $300:
P2 = (Revenue + $300) - Cost

3. Compare P2 to $600:

a. If P2 ≤ $600, you will not owe anything to your parents, and the most money you can hope to earn from your business is P2.

b. If P2 > $600, calculate the amount you owe to your parents:
Owe = 10% * (P2 - $600) (rounding to the nearest cent)

c. Subtract the amount you owe to your parents from the maximum profit:
Final Profit = P2 - Owe

By following these steps, you can determine the most money you can hope to earn from your business now and whether you will have to pay your parents.