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.
Do not include dollar signs in the solution Your answer
Let's define the variables:
x = number of cakes made and sold
P = total profit
The total cost to make x cakes is 14x dollars.
The total profit from selling x cakes is P = revenue - cost = 40x - 14x = 26x dollars.
We want to make a profit of at least $10,000. Therefore, we can set up the inequality:
26x ≥ 10000
To solve for x, divide both sides of the inequality by 26:
x ≥ 10000/26
x ≥ 384.62
Since we cannot make a fraction of a cake, we round up to ensure that the number of cakes made and sold is at least 385.
Thus, the solution to the inequality is:
x ≥ 385
Graph of the solution:
To graph this, we can plot a closed circle at x = 385 on a number line to indicate that it is included in the solution. Then, we can draw a line to the right to show all the values greater than or equal to 385.
-------------------●------------------------------>
385
This graph represents the solution to the inequality x ≥ 385.
Let's start by setting up the inequality.
Let "x" represent the number of cakes you need to sell.
The cost of making each cake is $14, so the total cost to make "x" cakes would be 14x dollars.
You are investing a total of $10,000, so the inequality becomes:
14x ≤ 10,000
To solve for "x," divide both sides of the inequality by 14:
x ≤ 10,000/14
x ≤ 714.29
Rounding this down to the nearest whole number, we get:
x ≤ 714
So, you need to sell a maximum of 714 cakes in order to stay within your investment budget.
Now, for the graph of the solution:
Graphically, this inequality represents a vertical line at x = 714. All values of "x" that are less than or equal to 714 lie on or to the left of this vertical line.
Therefore, the graph will be a vertical line passing through the point (714, 0) and extending downwards.
Please note that the vertical line should have an arrow at the bottom to indicate the direction of values less than or equal to 714.
To solve the inequality, we need to set up an expression using the given information. Let's assume the number of cakes you plan to make is represented by "x".
The total cost of making x cakes can be found by multiplying the cost per cake ($14) by the number of cakes (x). This can be written as: 14x.
Now, as per the given information, you have $10,000 to invest in your bakery business. Therefore, the amount you spend on making cakes should not exceed this investment. So, we can set up the inequality:
14x ≤ 10,000
To solve this inequality, we need to isolate the variable "x". Divide both sides of the inequality by 14:
x ≤ 10,000/14
Calculating the right side of the equation:
10,000/14 ≈ 714.28
Rounding to the nearest whole number, we get 714. Therefore, the solution to the inequality is:
x ≤ 714
To graph this solution on a number line, we can plot a shaded area to the left of or on the number 714, including the number itself. This represents all the possible values of x (the number of cakes you can make) that will not exceed your $10,000 investment.