Before infestation there were n trees, and after infestation there were n-x uninfested trees, if x maples were infested. No oaks were infested so the number of oaks stays the same.
Before infestation there were 5n/(5+9)=5n/14 oaks and 9n/14 maples.
After maple infestation, there are (n-x)/(3+11)=11(n-x)/14 oaks and 3(n-x)/14 uninfested maples.
So, since the number of oaks doesn’t change, 5n/14=11(n-x)/14, 5n=11n-11x, 11x=6n, x=6n/11. That means there are 6n/11 fewer maples after infestation.
We can express the number of trees after infestation as n-x=n-6n/11=5n/11.
3/14 of these trees are maples, that is, (3/14)(5n/11)=15n/154 uninfested maples. This has to be a whole number so n must be a multiple of 154. Call this integer multiple m, then the number of trees can be written 154m.
Number of maples before infestation=9n/14=99m.
Number of oaks=55m.
Number of uninfested maples after infestation=(3/14)(70m)=15m.
Number of infested maples=x=6n/11=(6/11)154m=84m.
To summarise, there were 99m maples and 55m oaks making 154m trees altogether. After infestation, there are 15m uninfested maples, making 70m uninfested trees altogether.
m=1 is the minimum value so there were 99 maples and all but 15 became infested, so the drop in numbers would be 84. The drop as a percentage is 84m/99m=28/33×100=84.85% (loss of 15.15%) approx., independent of m.
The drop as a ratio is 28:33, that is, 28 out of every 33 maples were infested; or 5:33 meaning 5 out of every 33 maples remain uninfested.
There were a minimum of 84 maples more before the bug problem than afterwards. The general answer is 84m where m>0 is an integer.
99:55=9:5 before; 15:55=3:11 after. Loss of 84.