First find the slope of the line using the two points:

So the equation has the form $y=4x+b$. Substitute one of the points, such as $(2,18)$:

so $b=10$. Therefore, the expression that represents the cost is

Let $n$ be the number of notebooks and $p$ be the number of pens. The total number of items gives $n+p=41$. The total amount of money gives $3n+2p=94$. Substitute $p=41-n$ into the second equation:

So, $12$ notebooks were sold.

Compare rows where only one fruit amount changes. From the first row to the second row, the number of pounds of grapes stays at $2$, and apples increase from $3$ lb to $5$ lb, so $2$ more pounds of apples cost $15.50-11.50=4.00$ dollars. That means apples cost $\frac{4.00}{2}=2.00$ dollars per pound.

Now compare the second row to the third row. The number of pounds of apples stays at $5$, and grapes increase from $2$ lb to $4$ lb, so $2$ more pounds of grapes cost $24.50-15.50=9.00$ dollars. Therefore, grapes cost $\frac{9.00}{2}=4.50$ dollars per pound.

So the price per pound of grapes is $\boxed{4.50}$.

Let $s$ be the number of student tickets and let $a$ be the number of adult tickets. The condition gives $a=3s-12$. Since the total number of tickets was $84$,

Substitute $3s-12$ for $a$:

This simplifies to

so

and

Therefore, the statement that must be true is that the theater sold $24$ student tickets.

Let the original width be $w$ feet, so the original length is $w+5$. Because the path is $1$ foot wide around the entire outside, each dimension increases by $2$ feet. The new dimensions are $(w+2)$ and $(w+7)$. Set up the area equation:

Expanding gives

so

This factors as

So $w=-14$ or $w=7$. A width must be positive, so the original garden is $7$ feet wide.