Respuesta :
92 adult tickets were sold
230 child tickets were sold
Explanation
Step 1
set the equations
let x represents the number of adult tickets sold
let y represents the number of child tickets sold
cost of adult ticket: 12
cost for child ticket : 5
so
a)On the first day of the fair, 322 tickets were sold
so
[tex]x+y=322\rightarrow equation(1)[/tex]b)total of $2,254
[tex]12x+5y=2254\rightarrow equation(2)[/tex]
Step 2
Solve the equations:
[tex]\begin{gathered} x+y=322\rightarrow equation(1) \\ 12x+5y=2254\rightarrow equation(2) \end{gathered}[/tex]a) isolate x in equation (1) and then replace in eqaution(2)
[tex]\begin{gathered} x+y=322\rightarrow equation(1) \\ x=322-y \end{gathered}[/tex]replace in equation (2)
[tex]\begin{gathered} 12x+5y=2254\rightarrow equation(2) \\ 12(322-y)+5y=2254 \\ 3864-12y+5y=2254 \\ \text{add like terms} \\ 3864-7y=2254 \\ 3864-2254=7y \\ 1610=7y \\ \text{divide both sides by 7} \\ \frac{1610}{7}=\frac{7y}{t} \\ 230=y \end{gathered}[/tex]b) now, replace the y value in equation (1) and solve for x
[tex]\begin{gathered} x+y=322\rightarrow equation(1) \\ x+230=322\rightarrow equation(1) \\ x=322-230 \\ x=92 \end{gathered}[/tex]therefore
92 adult tickets were sold
230 child tickets were sold
I hope this helps you
