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.
The equation that represents your total earnings, T, based on the price of your cake and how many you sell is:
T = $50 * x
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.
The revised inequality to reflect the new spending limit is:
T + $300 ≤ $600
Solving the inequality:
T + $300 ≤ $600
T ≤ $600 - $300
T ≤ $300
So, your total earnings must be less than or equal to $300 to stay within the new spending limit.
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 your total earnings must be less than or equal to $300, and you plan to sell each cake for $50, then the most money you can hope to earn from your business now is:
T ≤ $300
Since each cake is sold for $50, we can divide $300 by $50 to determine the maximum number of cakes you can sell:
$300 ÷ $50 = 6
Therefore, the most money you can hope to earn from your business now is $300, by selling a maximum of 6 cakes.
h)
Will you have to pay your parents?