many greetings to your teacher : how do you cut a circle into 4 equal circles ?
just by trying to adapt other similar problems into new forms and situations without actually thinking can lead to ridiculous results (like here).
also, "the number of circles" at the end, or after the original 1000 cut-outs ?
but let's just assume we can cut a circle into 4 equal circles, just as we can with a square (cut it into 4 equal squares).
then
x = number of circles
y = number of squares
x + y = 1000
x/2 × 4 = 4x/2 = 2x
out of x circles we have after the cutting
x/2 + 2x circles.
half the original circles remain the same, and the other half gets cut into 4 circles each.
y/7 × 4 = 4y/7
out of y squares we have after the cutting
6y/7 + 4y/7 squares.
6/7 of the original squares remain the same, the remaining 1/7 gets cut into 4 squares each.
as a result (twice as many circles than squares),
x/2 + 2x = 2×(6y/7 + 4y/7) = 2×10y/7 = 20y/7
x + 4x = 40y/7
5x = 40y/7
x = 8y/7
now, we can use that identity in the very first basic equation :
x + y = 1000
8y/7 + y = 1000
8y + 7y = 7000
15y = 7000
y = 7000/15 = 466.6666666...
x + y = 1000
x = 1000 - y = 1000 - 466.6666666... = 533.3333333...
that means there were originally (after the first 1000 cut-outs) 533.3333333... circles.
after the additional cuts we have then
533.3333333.../2 + 2×533.3333333... =
= 1,333.333333... circles.
this is just endlessly ridiculous.
we need integer numbers as result for this problem to make any sense.
so, let's assume the teacher knew what he/she was doing, and that cutting a circle into 4 equal parts destroys this circle, and is not creating squares either.
so, we end up with x/2 circles, and that is twice as much as the altogether created squares:
x/2 = 2×(6y/7 + 4y/7) = 20y/7
x = 40y/7
now with that we go into the main equation :
40y/7 + y = 1000
40y + 7y = 7000
47y = 7000
y = 7000/47 = 148.9361702...
x = 851.0638298...
still no integer solutions.
when we round, we would have 149 squares and 851 circles, but 851/2 and 149/7 are then not integers again.
so, either there are some typos in your question, or the whole original question is just nonsense, and we just did an arithmetic calculation exercise without any relation to the given scenario.