Respuesta :
Solution:
Let the number of adult tickets be
[tex]=x[/tex]Let the number of children tickets be
[tex]=y[/tex]The total number of tickets bought is
[tex]=9[/tex]Therefore,
The equation to represent the number of tickets will be
[tex]x+y=78\ldots\ldots\text{.}(1)[/tex]The cost of one adult ticket is
[tex]=10[/tex]The cost of children's tickets is
[tex]=8[/tex]The cost of x number of adult tickets will be
[tex]\begin{gathered} =10\times x \\ =10x \end{gathered}[/tex]The cost of y number of children tickets will be
[tex]\begin{gathered} =8\times y \\ =8y \end{gathered}[/tex]The total amount spent on the tickets is
[tex]=78[/tex]Therefore,
The equation to represent the total amount of money spent will be
[tex]10x+8y=78\ldots\ldots(2)[/tex]Combine the two equations together and then solve simultaneously
[tex]\begin{gathered} x+y=9\ldots\text{.}(1) \\ 10x+8y=78\ldots\ldots(2) \end{gathered}[/tex]Step 1:
Using the elimination method, make x the subject of the formula from equation (1) to form equation (3)
[tex]\begin{gathered} x+y=9 \\ x=9-y\ldots\ldots\text{.}(3) \end{gathered}[/tex]Step 2:
Substitute equation (3) in equation (2) to get the value of y
[tex]\begin{gathered} x=9-y\ldots\ldots\text{.}(3) \\ 10x+8y=78\ldots\ldots(2) \\ 10(9-y)+8y=78 \\ 90-10y+8y=78 \\ -2y=78-90 \\ -2y=-12 \\ \text{Divide both sides by -2} \\ \frac{-2y}{-2}=\frac{-12}{-2} \\ y=6 \end{gathered}[/tex]Step 3:
Substitute y=6 in equation (3) to get the value of x
[tex]\begin{gathered} x=9-y \\ x=9-6 \\ x=3 \end{gathered}[/tex]Hence,
The number of adult tickets jake bought = 3
