Question

The ratio of the number of senior tickets sold to the number of adult tickets is 2:3. The ratio of the number of adult tickets to the number of student tickets is 6:15. 24 senior tickets were sold, how many adults and students tickets were sold all together?

Answer 1

The total number of ticket booked altogether for students and adults is 126.

Explanation:

The ratio of Number of senior tickets sold: Number of adult tickets = 2:3.

or, Se : A = 2 : 3 ......... (1)

The ratio of Number of adult tickets : Number of student tickets = 6:15

or, A : St : 6 : 15 ........ (2)

Part - A : Given: Senior ticket sold = 24

Now, Let us assume the number of adult tickets sold = m

So Number of Senior tickets : Adult tickets = 24 : m .......... (3)

Comparing (1) and (3)

`(Se)/( A)   = (2)/(3)  = (24)/(m)\\ \implies  m = (24 * 3)/(2)   = 36`

Hence, the number of adult tickets booked is m = 36 tickets

Part - B

Adult tickets booked = 36 (From A)

Now, Let us assume the number of students tickets sold = n

So Number of Adult tickets : students tickets = 36 : n .......... (4)

Comparing (2) and (4)

`(A)/( St)   = (6)/(15)  = (36)/(n)\\ \implies  n = (36 * 15)/(6)   = 90`

Hence, the number of students tickets booked is n = 90 tickets

⇒ The number of adult tickets booked is 36 tickets

⇒Number of students tickets booked is 90 tickets

Hence, the total number of ticket booked altogether for students and adults is 90 + 36 =126.