Shayna's school is selling tickets to a fall musical. on the first day of tickets sales the school sold 14 adult tickets and 1 student ticket for a total of $107. the school took in $129 on the second day by selling 12 adult tickets and 5 student tickets. what is the price each of one adult ticket and one student ticket?
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The answer is: Each adult ticket is $7 and each student ticket is $9.

Step-by-step explanation:

Let a = the number of adult tickets. Let s = the number of student tickets.

For day 1:

14a + 1s = $107

Solve for s:

s = 107 - 14a

For day 2:

12a + 5s = $129

By substitution:

12a + 5(107 - 14a) = 129

12a + 535 - 70a = 129

-58a = 129 - 535

-58a = -406

a = -406 / -58 = $7 for adult tickets

Solve for s:

s = 107 - 14a

s = 107 - 14(7)

s = 107 - 98

s = $9 for student tickets

Proofs:

For day 1:

14a + 1s = $107

14(7) + 1(9) = 107

98 + 9 = 107

107 = 107

For day 2:

12a + 5s = $129

12(7) + 5(9) = 129

84 + 45 = 129

129 = 129

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answer: 7270

step-by-step explanation: