Daycare word problem

Question

A day care center in New Market currently has 7 assistant caregivers and 10 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

In about 3 months, there will be an equal number of assistant caregivers to senior caregivers, with 13 of each.

Since we know that there are initially 7 assistant caregivers and 10 senior caregivers, and we know that 2 assistant caregivers are hired per month while only 1 senior caregiver is hired per month, we can write an equation such that 2m + 7 = m +10, where m represents the number of months it has been since the initial number of each caregiver. Then, we can subtract m from both sides of the equation and subtract 7 from both sides of the equation so that m = 3. Therefore, it will take 3 months for there to be an equal number of assistant caregivers to senior caregivers.

To find the number of caregivers of each type in three months, simply subsitute 3 into either side of the equation:

2m + 7 =

2(3) + 7 =

13.

Therefore, there will be 13 assistant caregivers and 13 senior caregivers in three months.