Question

When Lisa started at her current job, her employer gave her 2 days of paid vacation time with a promise of 3 additional paid vacation days for each year she remains with the company to a maximum of 4 weeks of paid vacation time. Which equation below best represents the relationship between the number of years (x) Lisa has worked for her current employer and the number of paid vacation days (y) she has earned?

A) y = 2x + 3
B) y = 3x + 2
C) y = 2 + 3x
D) y = 3 + 2x

Answer 1

The correct equation representing the relationship between the number of years Lisa has worked and her earned paid vacation days is C) y = 2 + 3x. This accounts for the initial 2 days of vacation plus 3 additional days for each year worked, up to a maximum of 4 weeks.

Step-by-step explanation:

The relationship between the number of years Lisa has worked for her current employer and the number of paid vacation days she has earned can be modeled as a linear equation. Initially, Lisa is given 2 days of paid vacation. Each year she remains at the company, she earns an additional 3 days. So, after x years, Lisa will have earned 3x additional days on top of her initial 2 days. Therefore, the total number of vacation days y she has after x years is y = 2 + 3x, which makes option C) y = 2 + 3x the correct equation to represent this relationship.

It is important to note that the equation is valid as long as the total accumulated vacation does not exceed the maximum of 4 weeks (which is equivalent to 20 workdays since a typical workweek is 5 days). If Lisa accrues more than 4 weeks, then her vacation days are capped at that maximum.