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. Make sure to round to the nearest dollar.

* Do not include the dollar symbol in the inequality

Answer 1

Let x be the additional profit made.

The inequality can be revised as:
x - 300 ≤ 600

Simplifying the inequality:
x ≤ 600 + 300
x ≤ 900

Rounding to the nearest dollar, the solution is:
x ≤ $900

Answer 2

The inequality that reflects the new spending limit would be:

Income - Expenses ≤ $600 + $300

Let's solve this inequality step by step:

1. Simplify the expression:
Income - Expenses ≤ $900

2. Subtract the expenses from both sides of the inequality:
Income ≤ $900 + Expenses

Therefore, the revised inequality is: Income ≤ $900 + Expenses.

Please note that this inequality does not take into account the condition of owing 10% of earnings above $600 to your parents.

Answer 3

To revise the inequality to reflect the new spending limit, we need to consider the original inequality and add the additional $300. Let's denote the amount of additional profit as "x".

The original inequality based on the given information is:
x > 0

Now, considering the additional $300, the revised inequality becomes:
x + 300 > 0

To solve this inequality, we need to isolate "x" on one side of the equation.

First, let's subtract 300 from both sides of the inequality:

x + 300 - 300 > 0 - 300

Simplifying further, we have:

x > -300

Now, we have the revised inequality as:
x > -300

However, since profit cannot be negative, we can disregard the lower limit and consider the revised inequality as:
x > 0

Therefore, the solution to the revised inequality is:
x > 0

This means that you need to make more than $0 additional profit in order to trigger the agreement with your parents.