Question

The school that Emily goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold24 adult tickets and 3 student tickets for a total of $223.00. The school took in $152 on the second day by selling 7 adult tickets and 6 student tickets. What is the price each of one adult ticket and one student ticket?

Answer 1

Answer:

Step-by-step explanation:

Let x represent the price of one adult ticket.

Let y represent the price of one student ticket.

On the first day of ticket sales the school sold 24 adult tickets and 3 student tickets for a total of $223.00. This means that

24x + 3y = 223 - - - - - - - - - - - -1

The school took in $152 on the second day by selling 7 adult tickets and 6 student tickets. This means that

7x + 6y = 152 - - - - - - - - - - - - - -2

Multiplying equation 1 by 6 and equation 2 by 3, it becomes

144x + 18y = 1338

21x + 18y = 456

Subtracting, it becomes

123x = 882

x = 882/123

x = 7.17

Substituting x = 7.17 into equation 2, it becomes

7 × 7.17 + 6y = 152

50.19 + 6y = 152

6y = 152 - 50.19 = 101.81

y = 101.81/6 = 16.97