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.
x ≤ 300
If you still sell your item for the same price, what is the most money you can hope to earn from your business now?
$55,000
determine how much you will owe your parents.
You will owe your parents 10% of your earnings above $600. Since the most money you can hope to earn from your business is $55,000, and you have a spending limit of $300, your additional profit is $54,700 ($55,000 - $300 = $54,700).
Since this profit is above $600, you will owe your parents 10% of the earnings above $600, which is $54,100 ($54,700 - $600 = $54,100).
Therefore, you will owe your parents a total of $5,410 ($54,100 * 0.1 = $5,410).
To determine how much you will owe your parents, we need to calculate the amount you earn above $600 and then find 10% of that amount.
Since the most money you can hope to earn from your business now is $55,000, we need to determine how much you earn above $600. Subtracting $600 from $55,000 gives us $54,400.
Now, we need to find 10% of $54,400. We can do this by multiplying $54,400 by 0.10.
$54,400 * 0.10 = $5,440
Therefore, you will owe your parents $5,440.
Since the inequality is revised to state that x (the additional profit) should be less than or equal to $300, it means that the maximum additional profit you can make is $300.
Therefore, the most money you can hope to earn from your business now, including the additional $300, is the initial profit ($55,000) plus the additional profit ($300), which equals $55,300.
According to the given condition, if your additional profit is more than $600, you have to give your parents 10% of the amount above $600. In this case, since your additional profit is $300 (which is less than $600), you won't owe your parents anything.
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.
Let x represent the number of cakes you can make.
Since it takes 2.5 hours to make each cake, the total time (in hours) taken to make x cakes would be 2.5x.
Your time constraint is that the total time spent making cakes should be less than or equal to 200 hours.
Therefore, the inequality that represents your time constraint is:
2.5x ≤ 200
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?
To determine the maximum total profit, we need to consider the cost of making the cakes, the selling price, and the total number of cakes that can be made within the given time constraint.
Given that it costs $14 to make each cake and you are selling them for $50 each, the profit per cake is $50 - $14 = $36.
Since it takes 2.5 hours to make each cake and you have 200 hours available, dividing 200 by 2.5 gives us 80 cakes.
Therefore, the maximum total profit can be obtained by multiplying the profit per cake ($36) by the total number of cakes (80):
$36 * 80 = $2,880
Hence, the maximum total profit would be $2,880.
Does the investment you make and the time constraint allow you to profit from this venture?
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1 point
Yes, I can make more than $10,000
No, I make less than $10,000
Based on the information provided, the maximum total profit that can be obtained is $2,880, which is less than $10,000. Therefore, the investment and time constraint do not allow you to profit more than $10,000 from this venture. Hence, the answer is:
No, I make less than $10,000.