Since there are a adults and c children
Since there are 187 tickets sold
Then the number of adults and children is 187
Add a and c, then equate the sum by 187
[tex]a+c=187\rightarrow(1)[/tex]
Since the price of each adult's ticket is $25
Since the price of each child ticket is $13
Since the total revenue is $3223
Then multiply a by 25, c by 13, then add the products and equate the sum by $3223
[tex]25a+13c=3223\rightarrow(2)[/tex]
Now, we have a system of equations to solve it
Multiply equation (1) by -13 to make c equal in values and opposite in signs to eliminate it
[tex]\begin{gathered} -13(a)+-13(c)=-13(187) \\ -13a-13c=-2431\rightarrow(3) \end{gathered}[/tex]
Add equations (2) and (3)
[tex]\begin{gathered} (25a-13a)+(13c-13c)=(3223-2431) \\ 12a=792 \end{gathered}[/tex]
Divide both sides by 12
[tex]\begin{gathered} \frac{12a}{12}=\frac{792}{12} \\ a=66 \end{gathered}[/tex]
Substitute a by 66 in equation (1) to find c
[tex]66+c=187[/tex]
Subtract 66 from both sides
[tex]\begin{gathered} 66-66+c=187-66 \\ c=121 \end{gathered}[/tex]
The answers are:
a) The system of equations is
[tex]\begin{gathered} a+c=187 \\ 25a+13c=3223 \end{gathered}[/tex]
b) There were 66 adult tickets sold
c) There were 121 children's tickets sold
