Answer:
The price of a senior ticket is $12.
Step-by-step explanation:
Given:
Mr. Smith purchased 8 senior tickets and 5 child tickets for $136. Mr. Jackson purchased 4 senior tickets and 6 child tickets for $96.
Now, to get what is the price of a senior ticket.
Let the senior ticket be [tex]x[/tex] and the child ticket be [tex]y[/tex]:
So, according to question
[tex]8x+5y=136[/tex].........(1)
[tex]4x+6y=96[/tex]...........(2)
Now, we have system of equations:
Multiplying the equation (2) by -2 we get:
[tex]-8x-12y=-192[/tex].......(3)
Now, adding the equation (3) and (1) the variables and the numbers:
[tex]-8x-12y+8x+5y=-192+136[/tex]
[tex]-7y=-56[/tex]
Dividing both sides by -7 we get:
[tex]y=8[/tex]
Putting the value of y in equation (2) we get:
[tex]4x+6(8)=96[/tex]
[tex]4x+48=96[/tex]
On solving the equation we get:
[tex]x=12[/tex].
Therefore, the price of a senior ticket is $12.
