Question

A daycare center in Springdale currently has 1 assistant caregiver and 12 senior caregivers. Since demand is high, the owner is going to be hiring 2 assistant caregivers per month and 1 senior caregiver per month. Her goal is to have a larger staff, including an equal number of assistant caregivers and senior caregivers. How many of each type will there be? How long will that take?

Answer 1

Let the number of months it will take be n.

From the question, 2 assistant caregivers are hired every month.

So the total number of assistant caregivers in n months is 1 + 2n

From the question, 1 senior caregiver is hired every month.

So the total number of senior caregivers in n months is 12 + n

Since n is the number of months when the number of assistant caregivers equals the number of senior caregivers

Then

12 + n = 1 + 2n

12 - 1 = 2n -n

Which implies that n = 11.

12 + n = 12 + 11 = 23

Hence, there are 23 of each type and it will take 11 months