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.
f)
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
You can copy and paste the inequality sign below in your answer. ≥ < > ≤
The revised inequality would be:
Total Profit - $300 ≥ $600
To solve this inequality, we can add $300 to both sides of the inequality:
Total Profit ≥ $600 + $300
Total Profit ≥ $900
So the revised spending limit is a total profit of $900 or more.
The revised inequality representing the new spending limit is:
Total Profit - 300 ≤ 600
Solving for the inequality:
Total Profit ≤ 600 + 300
Total Profit ≤ 900
To revise the inequality from part a to reflect the new spending limit, we need to consider that if the additional profit exceeds $600, we have to give 10% of the earnings above $600 to our parents.
Let's start by revising the inequality. The original inequality was:
Profit ≥ $900
Since we now have an additional $300 from our parents, the revised inequality becomes:
Profit + $300 ≥ $900
Simplifying the inequality, we get:
Profit ≥ $600
This means that our new spending limit is to make a profit of at least $600.
Now, to solve this inequality, we need to subtract $600 from both sides:
Profit - $600 ≥ $600 - $600
Profit - $600 ≥ $0
The inequality is now:
Profit ≥ $0
The solution to this inequality is that we need to make a profit of at least $0.
Since making a profit of $0 or more is always possible, we can say that the solution to this inequality is all real numbers, or Profit ∈ (-∞, +∞).
Therefore, there are no limitations on the profit we can make with the additional $300 from our parents.