Marys school is selling tickets to a choral performance on the first day of ticket sales the school sold 6 senior tickets and 8 student tickets for a total of $102 the school took in $144 on the second day by selling 9 senior citizen tickets and 11 student tickets what is the price each for 1 senior ticket and 1 student ticket

Price of 1 senior ticket is $5 and 1 student ticket is $9.

Step-by-step explanation:

Let, the price for 1 senior ticket = $x and the price for 1 student

On the first day, the school sold 6 senior tickets and 8 student tickets.

Since, total amount received on the first day is $102.

We have, 6x + 8y = 102.

Also, on second day, the school sold 9 senior tickets and 11 student tickets.

Since, total amount received on the second day is $144.

We get, 9x + 11y = 144.

Thus, the system of equations becomes,

6x + 8y = 102

9x + 11y = 144

Dividing first equation by 2 gives, 3x + 4y = 51

i.e. the equations are,

3x + 4y = 51

9x + 11y = 144

Multiply first equation by 3 gives 9x + 12y = 153.

So, 9x + 12y = 153 and 9x + 11y = 144

Subtracting both equations, we get,

9x + 12y - 9x - 11y = 153 - 144

i.e. y = 9.

Substitute value of y in any equation,

3x + 4y = 51 i.e. 3x + 4 × 9 = 51 i.e. 3x = 51 - 36 i.e. 3x = 15 i.e. x = 5

Thus, the price of 1 senior ticket is $5 and 1 student ticket is $9.