Question

Ryan has his own business selling watches, and he wants to monitor his profit per watch sold. The expression ex.z-dn.net/?f=%5Cfrac%7B200x-300%7D%7Bx%7D" id="TexFormula1" title="\frac{200x-300}{x}" alt="\frac{200x-300}{x}" align="absmiddle" class="latex-formula"> models the average profit per watch sold, where x is the number of watches sold.
Ryan also earns money by selling colored watch bands with the watches he sells. The linear expression 100x – 50 models Ryan’s additional income. What is the expression that models the new average profit, including the bands? Note: To obtain the new average profit expression, add the linear expression to the original rational expression. Write the new profit expression as one fraction.

Answer 1

Answer:

$\frac{100x^2 +150x -300}{x}$

Step-by-step explanation:

Ryan gets  profit of selling x number watches = $\frac{200x - 300}{x}$

Also

Ryan earns money by selling colored watch bands = 100x - 50

To find the new average profit, we have to add the rational expression and linear expression.

=  $\frac{200x - 300}{x}$ + 100x - 50

$\frac{200x - 300}{x} + 100x - 50$

Here x is least common divisor. Taking x is a LCD, we get

$\frac{200x - 300 + x(100x - 50)}{x} \\=\frac{200x-300 + 100x^2 - 50x}{x} \\= \frac{100x^2 +150x -300}{x}$

The new profit expression $\frac{100x^2 +150x -300}{x}$

Answer 2

Answer:

(-x² + 99x +200)/x

Step-by-step explanation:

Profit per watch = (200 - x)/x

Profit per band = 100 – x

New profit = (200 - x)/x + 100 – x

New profit = (200 - x)/x + x(100 – x)/x

New profit = (200 - x + 100x – x²)/x

New profit = (-x² + 99x +200)/x