Question

A surfboard shaper has to limit the cost of development and production to ​$ 215 per surfboard. He has already spent ​$ 30,240 on equipment for the boards. The development and production costs are ​$ 143 per board. The cost per board is 143x+30,240/x dollars. Determine the number of boards that must be sold to limit the final cost per board to $ 215.

Answer 1

Answer:

420 boards.

Step-by-step explanation:

We have been given the formula for cost per board as $\frac{143x+30240}{x}$, where x represent number of boards. We are asked to find the number of boards that must be sold to limit the final cost per board to $215.

To find the number of boards, we will equate cost of x boards by 215 and solve for x as shown below:

$\frac{143x+30240}{x}=215$

$\frac{143x+30240}{x}*x=215*x$

$143x+30240=215x$

$143x-143x+30240=215x-143x$

$30240=72x$

$72x=30240$

$\frac{72x}{72}=\frac{30240}{72}$

$x=420$

Therefore, 420 boards must be sold to limit the final cost per board to $215.