Answer:
420 boards.
Step-by-step explanation:
We have been given the formula for cost per board as [tex]\frac{143x+30240}{x}[/tex], 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:
[tex]\frac{143x+30240}{x}=215[/tex]
[tex]\frac{143x+30240}{x}*x=215*x[/tex]
[tex]143x+30240=215x[/tex]
[tex]143x-143x+30240=215x-143x[/tex]
[tex]30240=72x[/tex]
[tex]72x=30240[/tex]
[tex]\frac{72x}{72}=\frac{30240}{72}[/tex]
[tex]x=420[/tex]
Therefore, 420 boards must be sold to limit the final cost per board to $215.
