h) With the revised inequality and the equation from part c, what is the new total profit, taking into account your additional $300 and any potential earnings above $600?
To find the new total profit, we need to calculate the earnings above $600 and subtract 10% of that amount if it exceeds $600.
Let's assume the number of cakes you sell is represented by x.
If you sell x cakes, the total earnings would be T = 50x.
But we need to take into account the condition of earning above $600. So, let's calculate the earnings above $600:
Earnings above $600 = T - 600
Now, if the earnings above $600 is greater than $600, we need to subtract 10% of that amount from the total earnings:
if (T - 600) > 600:
Total profit = T - 600 - (0.10 * (T - 600))
else:
Total profit = T - 600
Let's calculate the new total profit by substituting the value of T = 50x:
if (50x - 600) > 600:
Total profit = 50x - 600 - (0.10 * (50x - 600))
else:
Total profit = 50x - 600
Simplifying the equation:
if 50x - 600 > 600:
Total profit = 50x - 600 - (0.10 * (50x - 600))
else:
Total profit = 50x - 600
To solve this equation, let's find the value of x where the condition 50x - 600 > 600 is true:
50x - 600 > 600
50x > 1200
x > 1200/50
x > 24
Since we want the total profit considering the condition, x should be greater than 24.
So, the new total profit equation is:
if x > 24:
Total profit = 50x - 600 - (0.10 * (50x - 600))
else:
Total profit = 50x - 600
To calculate the new total profit, substitute the value of x with the maximum value from part b which is x ≤ 714:
if 714 > 24:
Total profit = 50(714) - 600 - (0.10 * (50(714) - 600))
else:
Total profit = 50(714) - 600
Total profit = $35,700 - $60 = $35,640
Therefore, the new total profit is $35,640.
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 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.
≥ < > ≤
x≤10,300
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
7 answers
determine how much you will owe your parents.
To determine how much you will owe your parents, we need to calculate 10% of the earnings above $600.
Let's assume the number of cakes you sell is represented by x.
If you sell x cakes, the total profit is given by the equation from part h:
Total profit = 50x - 600 - (0.10 * (50x - 600))
Now, we need to calculate 10% of the earnings above $600, which is (0.10 * (50x - 600)).
Let's simplify the equation:
10% of the earnings above $600 = 0.10 * (50x - 600)
To find how much you will owe your parents, we substitute the value of x with the maximum value from part b which is x ≤ 714:
10% of the earnings above $600 = 0.10 * (50(714) - 600)
10% of the earnings above $600 = 0.10 * (35700 - 600)
10% of the earnings above $600 = 0.10 * 35100
10% of the earnings above $600 = $3510
Therefore, you will owe your parents $3510.
Let's assume the number of cakes you sell is represented by x.
If you sell x cakes, the total profit is given by the equation from part h:
Total profit = 50x - 600 - (0.10 * (50x - 600))
Now, we need to calculate 10% of the earnings above $600, which is (0.10 * (50x - 600)).
Let's simplify the equation:
10% of the earnings above $600 = 0.10 * (50x - 600)
To find how much you will owe your parents, we substitute the value of x with the maximum value from part b which is x ≤ 714:
10% of the earnings above $600 = 0.10 * (50(714) - 600)
10% of the earnings above $600 = 0.10 * (35700 - 600)
10% of the earnings above $600 = 0.10 * 35100
10% of the earnings above $600 = $3510
Therefore, you will owe your parents $3510.
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
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
To revise the inequality from part a to reflect the new spending limit of an additional $300, we need to add $300 to the original spending limit.
Original inequality: 14x ≤ 10,000
Revised inequality: 14x ≤ 10,000 + 300
≤ 10,300
Simplifying the inequality, we have:
x ≤ 10,300 / 14
Using a calculator to round to the nearest whole number, we find:
x ≤ 736
So, the revised inequality is x ≤ 736.
Original inequality: 14x ≤ 10,000
Revised inequality: 14x ≤ 10,000 + 300
≤ 10,300
Simplifying the inequality, we have:
x ≤ 10,300 / 14
Using a calculator to round to the nearest whole number, we find:
x ≤ 736
So, the revised inequality is x ≤ 736.
determine how much you will owe your parents
To determine how much you will owe your parents, we need to calculate 10% of the earnings above $600.
Let's assume the number of cakes you sell is represented by x.
If you sell x cakes, the total profit is given by the equation from part h:
Total profit = 50x - 600 - (0.10 * (50x - 600))
Now, we need to calculate 10% of the earnings above $600, which is (0.10 * (50x - 600)).
Let's simplify the equation:
10% of the earnings above $600 = 0.10 * (50x - 600)
To find how much you will owe your parents, we substitute the value of x with the maximum value from part b which is x ≤ 714:
10% of the earnings above $600 = 0.10 * (50(714) - 600)
10% of the earnings above $600 = 0.10 * (35700 - 600)
10% of the earnings above $600 = 0.10 * 35100
10% of the earnings above $600 = $3510
Since you have additional $300 which is less than $3510, you will not owe your parents any money.
Therefore, you will not owe your parents any amount.
Let's assume the number of cakes you sell is represented by x.
If you sell x cakes, the total profit is given by the equation from part h:
Total profit = 50x - 600 - (0.10 * (50x - 600))
Now, we need to calculate 10% of the earnings above $600, which is (0.10 * (50x - 600)).
Let's simplify the equation:
10% of the earnings above $600 = 0.10 * (50x - 600)
To find how much you will owe your parents, we substitute the value of x with the maximum value from part b which is x ≤ 714:
10% of the earnings above $600 = 0.10 * (50(714) - 600)
10% of the earnings above $600 = 0.10 * (35700 - 600)
10% of the earnings above $600 = 0.10 * 35100
10% of the earnings above $600 = $3510
Since you have additional $300 which is less than $3510, you will not owe your parents any money.
Therefore, you will not owe your parents any amount.
1 answer