Respuesta :
General admission:784
Reserved seats:349
Explanation
Step 1
set the equations
let x represents the number of general admisions tickets sold
let y represents the number of greserved seats tickets sold
price of general admission: $ 2.0
price of reserved seat: $ 6.5
so
a)The receipts were $3836.50,hence
[tex]2x+6.5y=3836.5\Rightarrow equation(1)[/tex]B) also, the number of tickets sold is 1133, so
[tex]x+y=1133\Rightarrow equation(2)[/tex]Step 2
solve the equations
[tex]\begin{gathered} 2x+6.5y=3836.5\Rightarrow equation(1) \\ x+y=1133\Rightarrow equation(2) \end{gathered}[/tex]a) isolate x in equation (2) and replace in equation(1)
[tex]\begin{gathered} x+y=1133\Rightarrow equation(2) \\ \text{subtract y in both sides} \\ x+y-y=1133-y \\ x=1133-y \end{gathered}[/tex]now, replace in equation(1)
[tex]\begin{gathered} 2x+6.5y=3836.5\Rightarrow equation(1) \\ 2(1133-y)+6.5y=3836.5\Rightarrow equation(1) \\ \text{break the parenthesis} \\ 2266-2y+6.5y=3836.5 \\ \text{add like terms} \\ 2266+4.5y=3836.5 \\ \text{subtract 266 in both sides} \\ 2266+4.5y-2266=3836.5-2266 \\ 4.5y=1570.5 \\ \text{divide both sides by 4.5} \\ \frac{4.5y}{4.5}=\frac{1570.5}{4.5} \\ y=349 \end{gathered}[/tex]hence
the number of reserved seats sold is 349
b)now, replace the y value in equation (2) to find x
[tex]\begin{gathered} x+y=1133\Rightarrow equation(2) \\ x+349=1133 \\ \text{subtract 349 in both sides} \\ x+349-349=1133-349 \\ x=784 \end{gathered}[/tex]hence
the number of general admission tickets sold is 784
I hope this helps you
