Answer:
[tex]\begin{gathered} 245\text{ children tickets were sold.} \\ \text{ 720 adult tickets were sold.} \end{gathered}[/tex]
Step-by-step explanation:
To approach this situation, we need to create a system of linear equations.
Let x be the number of children
Let y be the number of adults
For equation 1)
Since the sum of the tickets sold are 965, it means children plus adults is 965
[tex]x+y=965[/tex]
For equation 2)
Since the price for children is $3, the adult ticket costs $5, and the total of tickets sold is $4,335:
[tex]3x+5y=4335[/tex]
Now, we can solve this by using the substitution method, isolating one of the variables in equation 1 and plugging it into equation 2.
[tex]y=965-x[/tex]
Plug it into equation 2:
[tex]3x+5(965-x)=4335[/tex]
Solve for x.
[tex]\begin{gathered} 3x+4825-5x=4335 \\ 5x-3x=4825-4335 \\ 2x=490 \\ x=\frac{490}{2} \\ x=245 \\ 245\text{ children tickets were sold.} \end{gathered}[/tex]
Knowing the value for x, we can plug it into equation 1, and solve for y.
[tex]\begin{gathered} y=965-245 \\ y=720\text{ } \\ \text{ 720 adult tickets were sold.} \end{gathered}[/tex]
