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.
* Do not include the dollar symbol in the inequality
Let's revise the inequality from part a to reflect the new spending limit:
600 + x ≤ 300
To solve this inequality, we need to isolate x on one side of the inequality sign.
Subtracting 600 from both sides:
x ≤ 300 - 600
x ≤ -300
Therefore, the solution to the inequality is x ≤ -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 the item for the same price, the most money you can hope to earn from your business now is $300.
h)
Will you have to pay your parents?
In this scenario, you will not have to pay your parents because you did not exceed the $600 additional profit threshold.
To revise the inequality from part a to reflect your new spending limit, you need to subtract the $300 your parents gave you from the total additional profit (x) and compare it to $600.
The revised inequality is:
x - $300 ≤ $600
To solve this inequality, you need to isolate the variable by adding $300 to both sides of the inequality:
x - $300 + $300 ≤ $600 + $300
x ≤ $900
Therefore, the solution to the inequality is:
x ≤ $900
This means that your additional profit (x) cannot exceed $900 in order to avoid owing your parents any portion of it.