A theater is selling tickets for a performance. Mr. Smith purchased 8 senior tickets and 5 child tickets for $136 for his friends and family. Mr. Jackson purchased 4 senior tickets and 6 child tickets for $96. What is the price of a senior ticket?
Accepted Solution
A:
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.