Hello,
Let me try helping you with this one.
This problem states that the ratio of certified teachers to non certified teachers must be kept above 9:2 for the school to qualify for federal funding.
The total number of teachers is 600.
We need to find the maximum number of non certified teachers that can be employed so that the school still qualifies for federal funding.
Now, when we try to increase the ratio above the minimum stated ratio, our split up of teachers into the two categories changes so that the number of non certified teachers reduces.
For example, let us take the ratio to be the minimum ratio, 9:2. Thus the number of certified teachers=9x and the number of non certified teachers is 2x.
9x+2x=600
x=54.54
2x~109
If we increase the ratio to 10:2, our total number of teachers becomes=12x and the number of non certified teachers becomes 100.
12x=600
x=50
2x=100
Thus, any increase in the ratio will work towards reducing the number of non certified teachers. The minimum ratio of certified to non-certified teachers needs to be used in order to get the maximum number of non-certified teachers.
Hence, the maximum number of non certified teachers that the school can employ and still qualify for federal funding is 109.
Hope this helps! Let me know in case of any further question.
megafan wrote:
To qualify for federal funding, a local school district must keep their ratio of certified teachers to non-certified teachers above \(9:2\). If the school district employs a total of 600 teachers, what is the maximum number of non-certified teachers they can employ and qualify for federal funding?
(A) 99
(B) 109
(C) 111
(D) 116
(E) 133