Question

A small company manufactures a certain item and sells it online. The company has a business model where the cost (C), in dollars, to make x items is given by the equation: C = (20/3)x + 50.The revenue (R), in dollars, made by selling x items is given by the equation: R = 10x

The break-even point is the point where the cost and revenue equations intersect. How many items must the company sell to break even? How do you know

A) The company must sell 3 items to break even because it's the point where the cost and revenue equations intersect.
B) The company must sell 4 items to break even because it's the point where the cost and revenue equations intersect.
C) The company must sell 5 items to break even because it's the point where the cost and revenue equations intersect.
D) The company must sell 10 items to break even because it's the point where the cost and revenue equations intersect.

Answer 1

The company must sell 15 items to break even.

Step-by-step explanation:

To find the break-even point, we need to set the cost and revenue equations equal to each other and solve for x:

(20/3)x + 50 = 10x

First, we can simplify the equation by multiplying both sides by 3 to eliminate the fraction:

20x + 150 = 30x

Then, we can subtract 20x from both sides:

150 = 10x

Finally, we divide both sides by 10:

x = 15

Therefore, the company must sell 15 items to break even.