Question

In a given corporation 1/6 of the hourly workers invest the

retirement plan and 1/2 of the salaried workers invest in the same
plan.
1/5 of the hourly workers invest the maximum allowed and 1/3 of the
salaried workers invest the maximum allowed.
If there are three times as many hourly workers as salaried
workers, what fraction of all the workers, who have invested in the
plan, invest the maximum allowable to the retirement plan.

Answer 1

Answer: 1/15 of all the workers invest the maximum allowable to the retirement plan.

Explanation:

x = hourly workers

y = salaried workers

1/6 of the hourly workers invest the retirement plan = 1/6 * x = x/6

1/2 of the salaried workers invest in the same plan. = 1/2 * y = y/2

1/5 of the hourly workers invest the maximum allowed = 1/5 * x/6 = x/30

1/3 of the salaried workers invest the maximum allowed = 1/3 * y/2 = y/6

there are three times as many hourly workers as salaried workers

x = 3y

Total workers: x + y = 3y + y = 4y

All workers that invest the maximum allowed: x/30 + y/6 = 3y/30 + y/6 =

3y + 5y = 8y = 4y

30 30 15

If all the workers are 4y, then 1/15 of all the workers invest the maximum allowable to the retirement plan.