Respuesta :
The total tickets bought is 7 and they spent $202
Each adult ticket costs $34 and each youth ticket costs $22
Let "x" be the number of adult tickets and "y" be the number of youth tickets.
You can calculate the total number of tickets as
[tex]x+y=7[/tex]And the total amounf of the purchase as the number of adults tickets multiplied by its price (34x) plus the number of youth tickets multiplied by its price (22y)
[tex]34x+22y=202[/tex]Now we have an equation system determined and can calculate the values of x and y.
1) Write the first equation in terms of one of the variables, for example in terms of x
[tex]\begin{gathered} x+y=7 \\ x=7-y \end{gathered}[/tex]Next replace that expression in the second equation and calculate the value of y
[tex]\begin{gathered} 34x+22y=202 \\ 34(7-y)+22y=202 \end{gathered}[/tex]Solve the multiplication by applying the distributive propperty of multiplication
[tex]\begin{gathered} 34\cdot7-34\cdot y+22y=202 \\ 238-34y+22y=202 \\ 238-12y=202 \end{gathered}[/tex]Pass 238 to the other side of the equation by applying the inverse operation to both sides of it, i.e. "238" is positive, so you have to subtract it
[tex]\begin{gathered} 238-238-12y=202-238 \\ -12y=-36 \end{gathered}[/tex]Divide both sides of the equation by -12 to get the value of y
[tex]\begin{gathered} -\frac{12y}{-12}=-\frac{36}{-12} \\ y=3 \end{gathered}[/tex]With this value calculate x as:
[tex]\begin{gathered} x=7-y \\ x=7-3 \\ x=4 \end{gathered}[/tex]They bought 4 adult tickets and 3 youth tickets (Answer B.)
