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.
Solve this inequality and choose the graph of the solution.
* Make sure to round to the nearest dollar.
Let's represent the number of cakes you will sell as x.
Since it costs $14 to make each cake and you want to invest $10,000, the total cost to make the cakes will be 14x.
Thus, the inequality representing the problem is:
14x ≤ 10,000
To solve this inequality, we can divide both sides by 14:
x ≤ 10,000/14
x ≤ 714.29
Since you cannot sell a fraction of a cake, you will have to round down to the nearest whole number:
x ≤ 714
Therefore, the solution to the inequality is x ≤ 714.
To graph this solution, we can plot a closed circle at x = 714 and shade the area to the left of the line, representing all the possible values of x that satisfy the inequality.
To find the inequality and graph the solution, we need to consider the total cost of making cakes and compare it with the amount of money you will invest.
Let's assume you make "x" cakes. The total cost of making cakes is given by multiplying the number of cakes made by the cost per cake, which is $14. Hence, the total cost (TC) can be expressed as:
TC = 14x
To earn a profit, the total cost of making cakes should be less than or equal to the amount of money you will invest, which is $10,000. So we can write the inequality as:
14x ≤ 10,000
Now, let's solve this inequality for "x":
x ≤ 10,000 / 14
x ≤ 714.28
Since we are dealing with whole cakes, we need to round down the result:
x ≤ 714
Therefore, the inequality for the number of cakes you can make is x ≤ 714.
Now, let's graph the solution on a number line:
0 714
The solution will be all the whole numbers from 0 to 714, including 0 and 714. However, it's not practical to have 0 cakes, so we can exclude that. Therefore, the graph of the solution will be an open circle at 0 and a closed circle at 714, with a solid line connecting them. All the whole numbers between 0 and 714, inclusive of 714, are part of the solution.
I'm sorry, as a text-based AI, I cannot provide an actual graph here. However, I hope the description helps you visualize it.
To solve the inequality, we need to consider the costs and the revenue generated from selling the cakes. Let's use the variable "x" to represent the number of cakes sold.
The revenue generated from selling the cakes can be found by multiplying the selling price per cake with the number of cakes sold. However, we are not provided information about the selling price. Therefore, we cannot directly calculate the revenue.
However, we can express the revenue in terms of the variable "x" and a certain selling price per cake. Let's assume the selling price per cake is "p" dollars.
The revenue can be calculated as:
Revenue = selling price per cake * number of cakes sold
Revenue = p * x
Now, let's consider the investment and cost involved. We know that the investment amount is $10,000, and it will cost $14 to make each cake. Therefore, the total cost (TC) can be calculated as:
TC = cost per cake * number of cakes sold
TC = $14 * x
To make a profit, we need the revenue to be greater than the total cost. So, the inequality can be written as:
Revenue - Total Cost > 0
px - 14x > 0
To solve this inequality, we need to isolate the variable "x". Let's do that step by step:
px - 14x > 0
Factor out the variable "x":
x(p - 14) > 0
Now, we have a product of two factors that is greater than zero. In order for this product to be greater than zero, one of the following conditions must be true:
1) Both factors are positive, or
2) Both factors are negative
Therefore, we have two cases to consider:
Case 1: Both factors are positive:
x > 0
p - 14 > 0
From the second inequality, we can solve for "p":
p > 14
This means that the selling price per cake should be greater than $14 for both factors to be positive. However, we don't have a specific value for the selling price, so we cannot determine the range of "x" in this case.
Case 2: Both factors are negative:
x < 0
p - 14 < 0
From the second inequality, we can solve for "p":
p < 14
This means that the selling price per cake should be less than $14 for both factors to be negative. Similar to Case 1, without a specific selling price, we cannot determine the range of "x" in this case.
As a result, considering the information given, we cannot determine a specific range for the number of cakes sold that would satisfy the given inequality. Therefore, we cannot choose a specific graph of the solution.
It is important to note that additional information about the selling price per cake or profit margins would be needed to determine a specific range or profit threshold.