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Answer :
Answer:
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.
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