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 my parents give me an additional $300 for my business, I will have to calculate my profits to determine if I owe them any amount.
Let's say my current profit without the additional $300 is X.
After receiving the additional $300, my profit would be X + $300.
To calculate the amount I owe my parents, I need to subtract $600 from my total profit.
If X + $300 - $600 is greater than $0, it means I have made more than $600 additional profit and I owe my parents 10% of the amount above $600.
Let's denote the additional profit as P and the amount owed to my parents as O.
P = (X + $300) - $600
If P is greater than $0, O = 0.10 * P
Therefore, if I make more than $600 additional profit, I would owe my parents 10% of the amount above $600.
To determine the amount you owe your parents if you make more than $600 additional profit, you need to calculate the earnings above $600 and then find 10% of that amount.
Let's break it down step by step:
1. Calculate your additional profit by subtracting $600 from the amount your parents are giving you, which is $300: $300 - $600 = -$300. Since the result is negative, it means you didn't make enough profit to owe any money to your parents.
2. Now, let's consider a scenario where you make more than $600 in additional profit, let's say $650:
a. Calculate the earnings above $600: $650 - $600 = $50.
b. Find 10% of the earnings above $600: $50 * 0.10 = $5.
Therefore, in this case, you would owe $5 to your parents.
Remember, you only owe them 10% on the earnings above $600. If your additional profit is less than or equal to $600, you don't owe them anything.
To calculate how much money you need to give your parents if you make more than $600 additional profit, follow these steps:
Step 1: Calculate your additional profit by subtracting $600 from the total amount of money you made from your business.
Step 2: Check if your additional profit is greater than zero.
Step 3: If your additional profit is greater than zero, multiply it by 10% (0.10) to find out how much money you owe your parents.
Step 4: Round the result from step 3 to the nearest cent, if necessary, for accuracy.
Step 5: The final result is the amount of money you owe your parents, which you calculated in step 4.
f)
Now that you have an additional $300, revise your inequality from part a to reflect your new spending limit. Solve this inequality.
Let's revise the inequality from part a to reflect the new spending limit with the additional $300:
Let C represent the amount of money you spend on your business.
The revised inequality is:
C ≤ W + 300
Now let's solve the inequality. I assume you were given your total profit (W) in part a.
To find the maximum amount of money you can spend on your business, subtract $300 from W:
C ≤ W - 300
This represents the new spending limit with the additional $300.
g)
If you still sell your item for the same price, what is the most money you can hope to earn from your business now?
If you still sell your item for the same price and you want to determine the maximum amount of money you can hope to earn from your business, you would calculate the total profit.
Let P represent the total profit you can hope to earn from your business.
To find the maximum total profit, you need to consider the additional $300 you received and the new spending limit, which is the amount you can spend on your business.
Let W represent your previous total profit (as mentioned in the question).
The maximum total profit would be:
P = W + 300
Adding the additional $300 to your previous total profit gives you the new maximum total profit you can hope to earn from your business.
h)
Will you have to pay your parents?
To determine if you have to pay your parents, you would need to compare the additional profit you make with the spending limit determined in part g.
If your additional profit is less than or equal to the spending limit, then you do not have to pay your parents. However, if your additional profit exceeds the spending limit, you will have to calculate the amount you owe them based on the terms given in part a.
Let's denote the additional profit as A and the amount owed to your parents as O.
If A is greater than the spending limit determined in part g, O = 0.10 * (A - spending limit).
Therefore, if your additional profit exceeds the spending limit, you will have to pay your parents 10% of the amount by which your additional profit exceeds the spending limit.