Question

Jonathan works at an advertising agency. When he was hired, he was given four days of paid vacation time. For each year that he worked there, he would gain another three days of paid vacation time to a maximum of 28 days.

Answer 1

a) The number of paid vacation days that Jonathan gets at the end of five years of employment is 19 days.

b) The model of the relationship between x, the number of years Jonathan has worked, and y, the number of paid vacation days earned, is y = 4 +3x.

c) Jonathan will reach the maximum number of paid vacation days allowable in 8 years.

Data and Calculations:

Initial paid vacation time for the first year = 4 days

Additional paid vacation time for an additional year = 3 days

Number of paid vacation time after 5 years = 19 days (4 + 3 x 5)

Number of years worked = x

Number of paid vacation days earned = y

Model of the relationship between x and y is y = 4 +3x.

If y = 28 days

x = (28 - 4)/3

x = 24/3

x = 8 years

Thus, the model of the relationship between x and y is y = 4 +3x.

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Question Completion:

a.) How many paid vacation days does he now get at the end of five years of employment?

b.) Using x for the number of years he has worked for the ad agency and y to represent the number of paid vacation days earned, write an equation to model the relationship between them.

c.) When will Jonathan reach the maximum number of paid vacation days allowable?