A daycare center in Oakland currently has 4 assistant caregivers and 12 senior caregivers. Since demand is high, the owner is going to be hiring 3 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 long will that take? How many of each type will there be?
System of equations X and y both equations
Let's assume that it will take "t" months to achieve the owner's goal.
Let's represent the number of assistant caregivers after "t" months as X, and the number of senior caregivers after "t" months as Y.
According to the given information, initially, there are 4 assistant caregivers and 12 senior caregivers.
So, after "t" months, the number of assistant caregivers will be 4 + 3t, and the number of senior caregivers will be 12 + 1t.
Since the owner's goal is to have an equal number of assistant caregivers and senior caregivers, we can write the following equation:
4 + 3t = 12 + 1t
Now, let's solve this equation to find the value of "t":
2t = 8
t = 4
Therefore, it will take 4 months to achieve the owner's goal.
Now, substitute the value of "t" in the expression for assistant caregivers to find the number of assistant caregivers after 4 months:
X = 4 + 3t
X = 4 + 3(4)
X = 4 + 12
X = 16
So, after 4 months, there will be 16 assistant caregivers.
Now, substitute the value of "t" in the expression for senior caregivers to find the number of senior caregivers after 4 months:
Y = 12 + 1t
Y = 12 + 1(4)
Y = 12 + 4
Y = 16
So, after 4 months, there will be 16 senior caregivers.
Therefore, after 4 months, there will be 16 assistant caregivers and 16 senior caregivers.