You want to start a bakery business to earn money. The total amount of money you will invest is $10,000. You will be selling cakes. It will cost you $14 to make each cake.

Question

a)
Write an inequality that represents the cost of making x amount of cakes should not exceed this investment.

* Do not include the dollar symbol in the inequality

You can copy and paste the inequality sign below in your answer.
≥ < > ≤

*
1 point
14x≤10,000

b)
Solve this inequality and choose the graph of the solution.
* Make sure to round to the nearest whole number.

Do not include dollar signs in the solution

*
1 point
x≤714

c)
You plan to sell each cake for $50. Write an equation that represents your total earnings, T, based on the price of your cake and how many you sell. Let x represent the number of cakes you sell.

* Use T and x as your variables

T=50x

d)
Using your answer from part b and your equation from part c, what is the most money you can hope to earn from your business?

$35,700

e)
Don’t forget that at the beginning of the process you had to spend some of your own money to get started. With the costs taken into account, what was your total profit?

$25,700

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

You can copy and paste the inequality sign below in your answer.
≥ < > ≤

blank

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?

$36,750

h)
Will you have to pay your parents If so, determine how much you will owe your parents.

Answer 1

Yes, you will have to pay your parents.

To determine how much you owe your parents, you need to calculate the amount of additional profit you make above $600 and then find 10% of that amount.

Let's assume you make an additional profit of $x.

If $x is greater than $600, you will owe your parents 10% of the amount above $600.

Therefore, you will owe your parents 10% of ($x - $600).

So, the amount you owe your parents is 10% * ($x - $600).

Answer 2

f)
Now that you have an additional $300, revise your inequality from part a to reflect your new spending limit. Solve this inequality.

Answer 3

The revised inequality from part a, taking into account the additional $300, would be:

14x ≤ 10,000 + 300

Simplifying the inequality:

14x ≤ 10,300

Now, solving for x:

x ≤ 735

Therefore, the revised solution is x ≤ 735.