Let's use the variables A for assistant caregivers and S for senior caregivers.
We know that currently there are 4 assistant caregivers, so A = 4.
We also know that currently there are 12 senior caregivers, so S = 12.
In order to have an equal number of assistant and senior caregivers, we want A = S.
The owner is going to be hiring 3 assistant caregivers per month, so the number of assistant caregivers will increase by 3 each month: A = 4 + 3t, where t represents the number of months.
Similarly, the owner is going to be hiring 1 senior caregiver per month, so the number of senior caregivers will increase by 1 each month: S = 12 + t.
We want A = S, so we can set up the equation: 4 + 3t = 12 + t.
Simplifying the equation, we get 2t = 8.
Dividing both sides of the equation by 2, we get t = 4.
This means it will take 4 months to have an equal number of assistant caregivers and senior caregivers.
Plugging in this value of t into the equations for A and S, we find:
A = 4 + 3(4) = 4 + 12 = 16 assistant caregivers.
S = 12 + 4 = 16 senior caregivers.
So after 4 months, there will be 16 assistant caregivers and 16 senior caregivers in total.
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
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