Question

Ryan has his own business selling watches, and he wants to monitor his profit per watch sold. The expression
`(200x-300)/(x)` 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

`(100x^2 +150x -300)/(x)`

Explanation:

Ryan gets profit of selling x number watches =
`(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.

=
`(200x - 300)/(x)` + 100x - 50

`(200x - 300)/(x) + 100x - 50`

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

`(200x - 300 + x(100x - 50))/(x) \\=(200x-300 + 100x^2 - 50x)/(x) \\= (100x^2 +150x -300)/(x)`

The new profit expression
`(100x^2 +150x -300)/(x)`

Answer 2

(-x² + 99x +200)/x

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