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. t represents the cost of making x amount of cakes should not exceed this investment.
Write an inequality that represents the cost of making x amount of cakes should not exceed this investment.
14x ≤ 10,000
Solve this inequality and choose the graph of the solution.
* Make sure to round to the nearest dollar.
714
Choose the graph of the solution to part b above.
The graph of the solution to the inequality 14x ≤ 10,000 is a line with a slope of -14 and a y-intercept at (0, 10000/14). The line intersects the x-axis at (714, 0) and the y-axis at (0, 714). So, the correct graph of the solution is the line y = 14x, with a shaded region below the line.
Since the cost of making each cake is $14, the total cost of making x cakes is given by 14x.
To represent that the cost of making x amount of cakes should not exceed the investment of $10,000, we can write the inequality:
14x ≤ 10,000
To solve this inequality, we divide both sides by 14:
x ≤ 10,000/14
Simplifying the right side:
x ≤ 714.2857
Rounding this to the nearest whole number:
x ≤ 714
Therefore, the solution to the inequality is x ≤ 714.
The graph of this solution would be a horizontal line at y = 714, with all the points on or below the line representing values of x that satisfy the inequality.
To solve the inequality 14x ≤ 10,000, we need to isolate the variable x.
Divide both sides of the inequality by 14:
x ≤ 10,000 / 14
Simplifying the right side:
x ≤ 714.29
Since we want to round to the nearest dollar, the solution is x ≤ 714 cakes.
For the graph of the solution, we will plot a closed dot at the point (714, 0) on a number line. Then, we will shade to the left of this point as the inequality is "less than or equal to." This represents all the values of x (number of cakes) that do not exceed the $10,000 investment.
The graph should show a closed dot at 714 and shading to the left.
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
The equation that represents your total earnings, T, based on the price of your cake and how many you sell is:
T = 50x
In this equation, T represents your total earnings, x represents the number of cakes you sell, and 50 represents the price of each cake.
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
To determine the most money you can hope to earn from your business, you need to consider the maximum value for the number of cakes you sell, x. In this case, as you are limited by the inequality x ≤ 714, the highest value you can use for x is 714.
Using the equation T = 50x, if you sell 714 cakes, the maximum amount of money you can hope to earn is:
T = 50 * 714
T = $35,700
Therefore, the most money you can hope to earn from your business is $35,700.