Final answer:
a. Tyler has earned 20 paid vacation days after 5 years. b. Tyler will reach the maximum number of paid vacation days allowable after approximately 9 years.
Step-by-step explanation:
a. To calculate the number of paid vacation days Tyler has earned after 5 years, we need to find the sum of his initial vacation days and the additional days earned each year. In the first year, Tyler earned 0 additional days, so he still has 5 days. In the second year, he earned 3 additional days, bringing the total to 8. In the third year, another 3 days were earned, making it 11 days. This pattern continues for each of the 5 years, so the calculation would be 5 + 3 + 3 + 3 + 3 + 3 = 20. Therefore, Tyler has earned 20 paid vacation days after 5 years.
b. To find when Tyler will reach the maximum number of paid vacation days allowable, we need to determine how many additional years it will take to earn enough days. Since Tyler can earn 3 additional days per year, we can set up the equation 5 + (3 * x) = 30, where x represents the number of additional years. Solving for x, we get 3x = 25, and dividing both sides by 3 gives x = 8.33. Since we can't have fractional years, we round up to the nearest whole number, which means it will take Tyler approximately 9 years to reach the maximum number of paid vacation days allowable.