children ticket:47
Adult ticket :13
Explanation
Step 1
set the equations
Let x represents the number of children's ticket
let y represent the number of adult tickets,
cost of a children ticket: $ 11
cost of a adult ticket: $ 17
so
a)she purchased 60 tickets, so
hence
[tex]x+y=60\Rightarrow equation(1)[/tex]
B)she spent a total fo $738, hence
[tex]11x+17y=738\Rightarrow equation(2)[/tex]
Step 2
Solve the equations
a) isolate the x value in equation (1) and replace in equation (2)
[tex]\begin{gathered} x+y=60\Rightarrow equation(1) \\ subtract\text{ y in both sides} \\ x+y-y=60-y \\ x=60-y \end{gathered}[/tex]
now,replace in equation(2)
[tex]\begin{gathered} 11x+17y=738\Rightarrow equation(2) \\ 11(60-y)+17y=738 \\ 660-11y+17y=738 \\ 6y+660=738 \\ \text{subtract 660 in boht sides} \\ 6y+660-660=738-660 \\ 6y=78 \\ \text{divide both sides by 6} \\ \frac{6y}{6}=\frac{78}{6} \\ y=13 \end{gathered}[/tex]
therefore,
the number of adult tickets is 13
b)now, replace the y value in equation (1) and solve for x
[tex]\begin{gathered} x+y=60\Rightarrow equation(1) \\ \text{replace} \\ x+13=60 \\ \text{subtract 13 in both sides} \\ x+13-13=60-13 \\ x=47 \end{gathered}[/tex]
therefore,
the number of children ticket 47
I hope this helps you
