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.

Question

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.

Revised inequality: x > 900

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

Answer 1

The most money you can hope to earn from your business now is $900.

Answer 2

To find out the most money you can hope to earn from your business with the additional $300 and the condition that you owe your parents 10% of your earnings above $600, we need to consider the revised inequality x > 900.

Let's break down the calculation step by step:

1. Subtract $600 from both sides of the revised inequality:
x - $600 > $900 - $600
x - $600 > $300

2. Add $600 to both sides of the inequality:
x > $900

This new inequality shows that your earnings (x) must be greater than $900 to owe your parents any money. If you earn less than or equal to $900, you don't owe them anything.

Since we know that your parents are giving you an additional $300, we can add this to the original amount you were already earning from your business. Therefore, the most money you can hope to earn now is:

$900 + $300 = $1200

So, the most money you can hope to earn from your business now is $1200.

Answer 3

To find the most money you can hope to earn from your business now, you need to consider the revised inequality and the additional condition given.

The revised inequality is x > 900, which means that your total profit, x, must be greater than $900.

The additional condition states that if you make more than $600 additional profit, you have to give your parents 10% of your earnings above $600.

To maximize your earnings, you need to stay as close as possible to the $900 threshold without exceeding it.

Based on this information, the maximum amount you can hope to earn from your business now is $900.