A hoverboard manufacturer has just announced the Glide $5$ hoverboard. The accounting department has determined that the cost to manufacturer the Glide $5$ hoverboard is $y=33.75 x+40256$ . The revenue equation is $y=96.65 x$ . What is the break even point for the Glide $5$ hoverboard?

Full solution

Q. A hoverboard manufacturer has just announced the Glide

5

hoverboard. The accounting department has determined that the cost to manufacturer the Glide

5

hoverboard is

y=33.75 x+40256

. The revenue equation is

y=96.65 x

. What is the break even point for the Glide

5

hoverboard?

Set Equations Equal: To find the break even point, we need to set the cost equation equal to the revenue equation and solve for $x$ , which represents the number of hoverboards. The cost equation is $y = 33.75x + 40256$ , and the revenue equation is $y = 96.65x$ .
Subtract $x$ Terms: Set the cost equation equal to the revenue equation: $33.75x + 40256 = 96.65x$ .
Combine Like Terms: Subtract $33.75x$ from both sides to get the $x$ terms on one side: $40256 = 96.65x - 33.75x$ .
Divide to Solve: Combine like terms: $40256 = 62.9x$ .
Perform Division: Divide both sides by $62.9$ to solve for $x$ : x = rac{40256}{62.9}.
Perform Division: Divide both sides by $62.9$ to solve for $x$ : $x = \frac{40256}{62.9}$ . Perform the division to find the value of $x$ : $x \approx 640$ .