Question

Samantha is a waitress and earns a weekly paycheck of $350 plus any tips she earns throughout the week. One week, Samantha noticed that she earned about $12 in tips each hour.

Let x represent the number of hours Samantha works during a week where her average hourly earnings is $22.

Write a rational equation that models this situation

Answer 1

`22=(350+12x)/(x)`

Explanation:

Samantha's weekly paycheck is $350 and she earns $12 in tips each hour. So, 12x represents the amount she earns in tips for working x hours. To find the total amount Samantha earns after working x hours, add the amount of her weekly paycheck and her amount earned in tips.

`350+12x`

Next, to find Samantha's average hourly earnings over the course of a week, divide the total amount that she earns in a week by the number of hours that she works, x.

`(350+12x)/(x)`

It is given that the average amount earned per hour for one particular week was $22. Therefore, set the above expression equal to 22 in order to create the rational equation that can be used to determine the number of hours Samantha worked that week.

`22=(350+12x)/(x)`

Answer 2

`(350+12x)/(x) =22`

Explanation:

Samantha's total earning per week are going to include the fix weekly wage of $350, plus whatever she gets from the tips. SInce what she gets from tips she noticed to be $12 per hour, if she works x hours during the week, the amount coming from tips only will be= $12*x

Therefore the total earning per week will add up to: $350 + $12*x

On the other hand, if we want to express her "average" hourly earnings, we need to divide the quantity above by the number of hours she works per week (we named such "x"):
`(350+12x)/(x)`

Therefore, the last expression that states that "Samantha's average hourly earnings is $22", can be written as:
`(350+12x)/(x)=22`