We are given the system of equations:
[tex]\begin{cases}x+y={350} \\ 3x+7y={2050}\end{cases}[/tex]
Where x is the number of child tickets sold and y is the number of adult tickets sold.
We want to find the number of adult tickets, the value of y.
To solve this, we can take the first equation and solve for x:
[tex]\begin{gathered} x+y=350 \\ . \\ x=350-y \end{gathered}[/tex]
And now substitute in the second equation:
[tex]3(350-y)+7y=2050[/tex]
And solve:
[tex]\begin{gathered} 1050-3y+7y=2050 \\ . \\ 4y=2050-1050 \\ . \\ y=\frac{1000}{4} \\ . \\ y=250 \end{gathered}[/tex]
Thus, the correct answer is option D. 250
