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.

Now that you have an additional $300, revise your inequality from part a to reflect your new spending limit. Solve this inequality.

Answer 1

The original inequality from part a was 600 < x, where x represents the additional profit. If we revise this to reflect the new spending limit with the additional $300 from the parents, the inequality becomes:

600 + 300 < x

Simplifying this inequality, we get:
900 < x

So, the revised inequality is x > 900.

To solve this inequality, we can say that the additional profit must be greater than $900 in order to trigger the condition of giving 10% of earnings above $600 to the parents.

Answer 2

The original inequality was: additional profit > $600

To revise the inequality with the new spending limit, we add the $300 that your parents are giving you:

additional profit + $300 > $600

To solve this inequality, we will isolate the additional profit on one side:

additional profit > $600 - $300
additional profit > $300

So, the revised inequality is: additional profit > $300.

Answer 3

To revise the inequality to reflect the new spending limit, we need to consider the original condition that you have to give 10% of earnings above $600. Let's first define some variables:

Let x be the additional profit you make above $600.
Let y be the amount you will owe to your parents in dollars.

With this in mind, we can revise the inequality as follows:

If your additional profit is less than or equal to $300 (the amount your parents are giving you), then the revised inequality can be written as:

x ≤ 300

However, if your additional profit is greater than $300, you need to consider the condition that you would owe 10% of the earnings above $600 to your parents. So the revised inequality becomes:

300 < x ≤ 600 + (0.10)(x - 600)

Now let's solve this revised inequality:

300 < x ≤ 600 + (0.10)(x - 600)

First, multiply the 0.10 with (x - 600):

300 < x ≤ 600 + 0.10x - 60

Combine like terms:

300 < x ≤ 0.10x + 540

Now, let's isolate the x terms:

-0.10x + 300 < x ≤ 540

Add 0.10x to both sides:

300 < 1.10x ≤ 540

Divide by 1.10:

300/1.10 < x ≤ 540/1.10

This simplifies to:

272.73 < x ≤ 490.91

So, the solution to the inequality is:

272.73 < x ≤ 490.91

This means that if your additional profit is greater than $272.73 but less than or equal to $490.91, then you will need to give 10% of the earnings above $600 to your parents.