Question

a surfboard shaper has to limit the cost of development and production to $214 per surfboard. he has already spent $24,304 on equipment for the boards. the development and production cost is $158 per board. the cost per board is $\frac{158x + 24,304}{x}$ dollars. determine the number of boards that must be sold to limit the final cost per board to $214. how many boards must be sold to limit the cost per board to $214?

Explanation:

Step1: Set up the cost - equation

We are given that the cost per board is $\frac{158x + 24304}{x}$, and we want this cost to be equal to 214. So, we set up the equation $\frac{158x+24304}{x}=214$.

Step2: Multiply both sides by x

To get rid of the denominator, we multiply both sides of the equation by $x$: $158x + 24304=214x$.

Step3: Rearrange the equation

Subtract $158x$ from both sides: $24304=214x - 158x$.

Step4: Simplify the right - hand side

Combine like terms: $24304 = 56x$.

Step5: Solve for x

Divide both sides by 56: $x=\frac{24304}{56}=434$.

Answer:

434