Question

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?

Answer 1

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 $x$ and the child ticket be $y$:

So, according to question

$8x+5y=136$.........(1)

$4x+6y=96$...........(2)

Now, we have system of equations:

Multiplying the equation (2) by -2 we get:

$-8x-12y=-192$.......(3)

Now, adding the equation (3) and (1) the variables and the numbers:

$-8x-12y+8x+5y=-192+136$

$-7y=-56$

Dividing both sides by -7 we get:

$y=8$

Putting the value of y in equation (2) we get:

$4x+6(8)=96$

$4x+48=96$

On solving the equation we get:

$x=12$.

Therefore, the price of a senior ticket is $12.