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

Answer:

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

Step-by-step 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)

$\frac{Se}{ A} = \frac{2}{3} = \frac{24}{m}\\ \implies m = \frac{24 \times 3}{2} = 36$

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)

$\frac{A}{ St} = \frac{6}{15} = \frac{36}{n}\\ \implies n = \frac{36 \times 15}{6} = 90$

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.