Question

A new hospital in Springfield starts out with 11 junior residents and 5 senior readings on its staff. Management plans to to hire additional personnel at a rate of 1 junior resident per month and 3 senior residents per month. Eventually there will be an equal number of each on the hospital staff. How long will that take? How many of each type will be there be?

Answer 1

3 months

14 of each type of staff

Explanation:

Starting employees

Junior residents = 11

Senior readings = 5

Additional personnel at a rate of 1 junior resident per month and 3 senior residents per month

Junior residents = 11 + m

Senior readings = 5 + 3m

Where,

m = number of months

How long will that take?

Equate both expression

11 + m = 5 + 3m

11 - 5 = 3m - m

6 = 2m

Divide both sides by 2

m = 6/2

= 3

m = 3 months

Junior residents = 11 + m

= 11 + 3

= 14

Senior readings = 5 + 3m

= 5 + 3(3)

= 5 + 9

= 14