Question 896·Hard·Math

Let $x$ be the number of plants that are both native and flowering. The condition “among the flowering plants” means the $\frac{3}{5}$ describes that group only. For every $3$ native flowering plants, the other $2$ flowering plants are nonnative, so the nonnative flowering count is $\frac{2}{3}x$. The group named after “among” supplies the denominator, not all $240$ plants.

Now the condition switches to among the native plants. Since $\frac{1}{2}$ of them are flowering, the other $\frac{1}{2}$ are nonflowering. The two halves have equal counts, so the native nonflowering count is $x$, not $\frac{1}{2}x$.

The four nonoverlapping groups account for all $240$ plants. Add native flowering, nonnative flowering, native nonflowering, and the given nonnative nonflowering count:

Subtracting $72$ and calling everything left flowering would also count the native nonflowering plants.

Type $x_{1}+\frac{2}{3}x_{1}+x_{1}+72\sim240$ in Desmos. The $x_{1}$ and $\sim$ tell Desmos to solve for a value rather than graph $x$. Under PARAMETERS, it shows $x_{1}=63$. Since $x$ counts plants that are both native and flowering, the garden has $63$ such plants. Grid in 63.