Question

a surfboard shaper has to limit the cost of development and production to $134 per surfboard. he has already spent $88,375 on equipment for the boards. the development and production costs are $107 per board. the cost per board is $\frac{107x + 88375}{x}$ dollars. determine the number of boards that must be sold to limit the final cost per board to $134.
how many boards must be sold to limit the cost per board to $134?

Explanation:

Step1: Set up the cost - equation

Let $x$ be the number of boards. The total cost $C$ is the sum of the fixed cost ($86375$) and the variable cost ($157x$). The average cost per board $A$ is $\frac{157x + 86375}{x}$. We want $A = 334$. So, we set up the equation $\frac{157x+86375}{x}=334$.

Step2: Multiply both sides by $x$

Multiply both sides of the equation $\frac{157x + 86375}{x}=334$ by $x$ (assuming $x
eq0$) to get $157x+86375 = 334x$.

Step3: Rearrange the equation

Subtract $157x$ from both sides: $86375=334x - 157x$.

Step4: Simplify the right - hand side

$334x-157x = 177x$, so the equation becomes $86375 = 177x$.

Step5: Solve for $x$

Divide both sides by $177$: $x=\frac{86375}{177}\approx488$.

Answer:

$488$