b) 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
Choose the graph of the solution to part b above
A -50 0 50 100 150 200 (200 has the dot) 250
B -100 0 100 200 300 400 500 600 700 (700 has the dot) 800
C -50 0 50 100 150 200 (200 has the open dot)
D -400 -200 0 200 400 600 (has a open dot between 600 and 800) 800 1,000 1,200
O Option A
O Option B
O Option C
O Option D
Option C
To solve the inequality, we need to consider the total amount of money invested ($10,000) and the cost to make each cake ($14). Let's represent the number of cakes sold as 'x'.
The amount of money taken in from selling the cakes would be the selling price per cake (which we don't have) multiplied by the number of cakes sold. Since we are interested in maximizing the profit, we need to subtract the total cost from the total earnings and set it to be greater than or equal to $0.
Mathematically, this can be written as:
($14 * x) - $10,000 ≥ $0
Next, we can solve for 'x':
$14 * x ≥ $10,000
x ≥ $10,000 / $14
x ≥ 714.29
Since we are dealing with a discrete number of cakes, we round this down to the nearest whole number.
x ≥ 714
Now let's examine the graphs provided. Option B is the graph that shows the values that are greater than or equal to 714.
Therefore, the correct answer is Option B.
To solve the inequality, we need to examine the given information.
Let's assume x represents the number of cakes you make and sell.
The total amount of money you will invest is $10,000.
It will cost you $14 to make each cake.
So, the cost of making x cakes is 14x dollars.
To earn money, the money earned needs to be greater than or equal to the money invested, i.e., 14x ≥ 10,000.
To find the solution, we need to solve this inequality for x.
Dividing both sides of the inequality by 14 gives us:
x ≥ 10,000 / 14
Now, we can calculate this value:
x ≥ 714.28571
Since we can't have a fraction of a cake, we round this up to the nearest whole number:
x ≥ 715 (rounded to the nearest whole number)
This means you need to make and sell at least 715 cakes to earn back the $10,000 investment.
Now, let's compare the solutions with the given graphs:
Option A: The graph does not intersect or include the value x = 715.
Option B: The graph intersects at x = 715 (has the dot).
Option C: The graph has an open dot at x = 715, so it is not included in the solution.
Option D: The graph has an open dot between 600 and 800, so it is not included in the solution.
Therefore, the correct graph of the solution to the inequality is:
O Option B