price of the gift

Let $x$ be the number of students and $y$ be the cost of the gift in $.

Then the two equations are

$2x+4=y$ $\color{#D61F06}(1)$

$3x-3=y$ $\color{#D61F06}(2)$

From these two equations, we know that $y=y$ , so

$2x+4=3x-3$

$4+3=x$

$x=7$

Substituting $x=7$ in any of the two equations yields, $y=18$ .

Let $s$ be the number of students and $g$ the price of the gift.

$\begin{cases} 2s = g - 4 \\ 3s = g + 3 \end{cases}$

Just solve for $g.$

$s = \frac{g - 4}{2} \color{#3D99F6}\text{ (from the first equation)} \\ 3 \ast \frac{g - 4}{2} = g + 3 \\ 3 (g - 4) = 2 (g + 3) \\ 3g - 12 = 2g + 6 \\ \boxed{g = 18}$