there are 16 junior high students in the brewster town swimming club. a student is chosen at random to be…

Explanation:

Step1: Calculate number of 7th - graders

Since probability of choosing a 7th - grader is $\frac{1}{2}$ and total number of students is 16, number of 7th - graders is $16\times\frac{1}{2}=8$.

Step2: Let number of 9th - graders be $x$ and 8th - graders be $y$

We know $x + y+8 = 16$, so $x + y=8$. Also $y>x$ and $x>0$.

Step3: Find greatest possible $x$

Since $y>x$ and $x + y = 8$, when $y=x + 1$, we have $x+(x + 1)=8$, $2x=7$, $x = 3.5$. But $x$ is an integer, so greatest integer value of $x$ such that $y>x$ is $x = 3$.

Step4: Find least possible $x$

Since $x>0$ and $x$ is an integer, the least possible value of $x$ is 1.

Answer:

3 1