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.
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 dollar.
Do not include dollar signs in the solution
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
***Make sure to have x and an inequality sign in your answer
*
1 point
714.28 rounded to 714.29 x ≤ 714
Choose the graph of the solution to part b above.
1 point
Captionless Image
Option A
Option B
Option C
Option D
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
*
1 point
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?
*
1 point
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?
*
1 point
Did you make money or lose money?
*
1 point
Make Money
Lose Money
c) The equation that represents the total earnings, T, based on the price of each cake and the number of cakes sold is T = 50x.
d) Using the answer from part b, where x ≤ 714, and the equation from part c, the most money that can be earned from the business is T = 50(714) = $35,700.
e) To calculate the total profit, we need to subtract the total amount invested from the total earnings.
Total Profit = Total Earnings - Total Investment
Total Profit = $35,700 - $10,000 = $25,700.
The business made money with a total profit of $25,700.
a) 14x ≤ 10,000
b) The solution to the inequality 14x ≤ 10,000 is x ≤ 714.29 (rounded to 714).
c) T = 50x
d) Using the maximum number of cakes you can sell, x = 714, the most money you can hope to earn is T = 50 * 714 = $35,700.
e) To calculate the total profit, we need to subtract the investment cost (10,000) from the total earnings (35,700).
Total Profit = Total Earnings - Investment Cost
Total Profit = $35,700 - $10,000
Total Profit = $25,700
Therefore, you made money with a total profit of $25,700.
a) The inequality that represents the cost of making x amount of cakes should not exceed the investment of $10,000 is:
14x ≤ 10,000
b) To solve this inequality and find the maximum number of cakes you can make with a $10,000 investment, divide both sides of the inequality by 14:
x ≤ 10,000 / 14 ≈ 714.29
Rounding to the nearest whole number, x ≤ 714.
The graph of this solution would show a line starting at the origin (0, 0) and extending horizontally up to the point (714, 0) on the x-axis.
c) The equation that represents your total earnings (T) based on the price of each cake ($50) and the number of cakes sold (x) is:
T = 50x
d) Using the solution from part b (x ≤ 714) and the equation from part c (T = 50x), we can find the most money you can hope to earn by substituting the maximum value of x into the equation:
T = 50 * 714 ≈ $35,700
The most money you can hope to earn from your business is approximately $35,700.
e) To calculate the total profit, we need to subtract the cost of making the cakes from the total earnings. The cost of making each cake is $14, and the equation from part c gives the total earnings as $35,700:
Profit = Total Earnings - Cost
Profit = $35,700 - ($14 * 714) ≈ $25,996
The total profit is approximately $25,996. Since the profit is positive, you made money from your business.