The school that Danielle goes to is selling tickets to a spring musical. On the first day of ticket sales the school sold 10 adult tickets and 13 student tickets for a total of $234. The school took in $97 on the second day by selling 5 adult tickets and 4 student tickets. What is the price each of one adult ticket and one student ticket?

Price of Adult tickets =$ 13

Price of student tickets =$ 8

Step-by-step explanation:

Lets us represent the price of adult tickets = x

The price of student tickets = y

On the first day of ticket sales the school sold 10 adult tickets and 13 student tickets for a total of $234.

= 10 × x + 13 × y = $234

= 10x + 13 y = 234

The school took in $97 on the second day by selling 5 adult tickets and 4 student tickets.

5 × x + 4 × y = $97

= 5x + 4y = 97

Hence:

10x + 13y = 234Equation 1

5x + 4y = 97 Equation 2

We solve by elimination method

Multiply the equation 1 by 5 and equation 2 by 10 which are the coefficient of x

10x + 13y = 234Equation 1 × 5

5x + 4y = 97 Equation 2 × 10

50x + 65y = 1170Equation 3

50x + 40y = 970 Equation 4

Subtract Equation 4 from Equation 3

25y = 200

y = 200/25

y = 8

Therefore the price of student ticket = $8

Note that

5x + 4y = 97 Equation 2

5x + 4 × 8 = 97

5x = 97 + 32

5x = 65

x = 65/5

x = 13

Therefore price of adult tickets = $13

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step-by-step explanation: