# Carla Company began operations on January 2, 2016. It employs 6 individuals who work for 8-hour...

## Question:

Carla Company began operations on January 2, 2016. It employs 6 individuals who work for 8-hour days and are paid hourly. Each employee earns 11 paid vacation days and 8 paid sick days annually. Vacation days may be taken after January 15 of the year following the year in which they were earned. Sick days may be taken as soon as they are earned; unused sick days accumulate. Additional information is as follows:

Actual Hourly Wage Rate Vacation Days Used by Each Employee Sick Days Used by Each Employee
2016 2017 2016 2017 2016 2017
$11$12 0 10 6 7

Carla Company has chosen to accrue the cost of compensated absences at rates of pay in effect during the period when earned and to accrue sick pay when earned.

Provide a step-by-step solution explaining how to calculate step 2.

## Word Problems:

The key to solving most mathematical word problems is to understand the variables. The problem asks for the vacation pays and sick pays for the year 2016 and 2017, where each year has different hourly rates.

We can solve the problem by first calculating the vacation pay and then the sick pay. Since the vacation pay can be calculated in the year following the year in which they were earned, it's intuitive that during the year 2016, there's no vacation used.

Now, the tricky part is calculating the rate of vacation pay during the period it was earned, that is, the year before. Looking at the table, on 2017, there were 10 vacation days used by each employee:

{eq}Total \ Vacation \ Pay = 6\:Employees\:\times 8\:\dfrac{Hours}{Day}\times 10\:\dfrac{Days}{Employee}\:\times \dfrac{11}{Hour}\\ \ \\ Total \ Vacation \ Pay = 5,280 {/eq}

To solve for the sick days, we add the sick days for 2016 and 2017. Note that each year has a different hourly wage:

{eq}Total \ Sick \ Pay = 6\:Employees\:\times 8\:\dfrac{Hours}{Day}\times 6\:\dfrac{Days}{Employee}\:\times \dfrac{11}{Hour}+6\:Employees\:\times \:8\:\dfrac{Hours}{Day}\times \:7\dfrac{Days}{Employee}\:\times \:\dfrac{12}{Hour}\\ \ \\ Total \ Sick \ Pay = 7,200 {/eq}