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.
≥ < > ≤
*Make sure to solve the inequality and write x and an inequality sign in your answer.
*
1 point
Choose the graph of the solution to part f above
*
1 point
Captionless Image
Option A
Option B
Option C
Option D
Other:
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?
*
1 point
h)
Will you have to pay your parents?
*
1 point
Yes
No
If so, determine how much you will owe your parents.
*
1 point
i)
You are trying to decide if it is worth the investment to make the cakes if it takes 2.5 hours to make each cake and you have 200 hours this summer to devote to creating your product. Write an inequality that represents your time constraint.
*Use x as the variable
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
*
1 point
j)
Solve your inequality from part i
**Make sure to have x and an inequality sign in your answer
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
*
1 point
Choose the graph of the solution from part j above. *
1 point
Option 1
Option 2
Option 3
Option 4
Other:
k)
Remember it costs $14 to make the cakes and you are selling them for $50 each. If you only spend the 200 hours making the cakes, what was your maximum total profit?
*
1 point
Does the investment you make and the time constraint allow you to profit from this venture?
*
1 point
Yes, I can make more than $10,000
No, I make less than $10,000
f) The revised inequality is x + 300 ≥ 600.
Solving the inequality, x ≥ 300.
g) The most money you can hope to earn from your business now is $300 + $600 = $900.
h) No, you will not have to pay your parents since you are not making more than $600 profit.
i) The inequality that represents the time constraint is 2.5x ≤ 200.
j) Solving the inequality, x ≤ 80.
k) If you only spend the 200 hours making the cakes, your maximum total profit would be ($50 - $14) * 80 = $2,880.
The investment and time constraint do allow you to profit from this venture, but the profit is less than $10,000.