Question

Elisa school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 8 adult tickets and 3 children tickets for a total of $119. The school took in $135 on the second day by selling 10 tickets and 1 child ticket. What is the price each of one adult ticket and one child ticket?

Answer 1

ANSWER:

Fare of adult tickets is $13 and fare of child tickets is $5.

SOLUTION:

Given, Elisa school is selling tickets to the annual talent show.  

Let, adult ticket fare be x and child ticket fare be y.

On the first day of ticket sales the school sold 8 adult tickets and 3 children tickets for a total of $119.

Then, 8x + 3y = 119 --- (1)

The school took in $135 on the second day by selling 10 adult tickets and 1 child ticket.  

Then, 10x + y = 135

y = 135 – 10x ---- (2)

Now, substitute y value in (1)

8x + 3(135 – 10x) = 119

8x + 3 × 135 – 3 × 10x = 119

8x + 405 – 30x = 119

405 – 119 = 30x – 8x

286 = 22x

x = $\frac{268}{22}$

x = 13

Now, substitute x value in (2)

y = 135 – 10(13)

y = 135 – 130  = 5

Hence, fare of adult tickets is $13 and fare of child tickets is $5.