PLEASE HELP!!! I DON´T KNOW WHAT TO DO!!

Question

A daycare center in Seaside currently has 9 assistant caregivers and 6 senior caregivers. Since demand is high, the owner is going to be hiring 1 assistant caregiver per month and 2 senior caregivers per month. Her goal is to have a larger staff, including an equal number of assistant caregivers and senior caregivers. How long will that take? How many of each type will there be?

After _____________ months, there will be_________  of each type of caregiver

Answer 1

Begin with an equation of your goal: the same number of seniors and assistants. Let S = seniors and A = assistants. We're starting out with 6 seniors and 9 assistants. So we can say 6 + S = 9 + A. We're told that each month twice as many seniors as assistants will be hired. So we can say S = 2A and 6 + 2A = 9 + A, If we think of the seniors and assistants as new workers, we can say 6 + 2W = 9 + W and solve for W, plug the value of W into our equation, and get the (equal) number of the two type of employees. Since W represents the total number of assistants hired at one per month, W is also the total number of months it will take to get them.

Answer 2

If m = the number of months, each month has 9 + m assistant caregivers and 6 + 2m senior caregivers.

9 + m = 6 + 2m

m = 3

9 + m = 9 + 3 = 12

6 + 2m = 6 + 2(3) = 6 + 6 = 12

Boom

After 3 months, there will be 12 of each type of caregiver.