Q:

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?

Accepted Solution

A:
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 =  6:15or, A : St  : 6 : 15   ........  (2)Part - A   :   Given:   Senior ticket sold  = 24Now, Let us assume the number of adult tickets sold  = mSo Number of Senior tickets :  Adult tickets   = 24  :  m  ..........  (3)Comparing (1) and (3)[tex]\frac{Se}{ A}   = \frac{2}{3}  = \frac{24}{m}\\ \implies  m = \frac{24 \times 3}{2}   = 36[/tex]Hence, the number of adult tickets booked is  m =  36 ticketsPart - BAdult tickets booked  = 36 (From A)Now, Let us assume the number of students tickets sold  = nSo Number of Adult tickets :  students tickets   = 36  :  n  ..........  (4)Comparing (2) and (4)[tex]\frac{A}{ St}   = \frac{6}{15}  = \frac{36}{n}\\ \implies  n = \frac{36 \times 15}{6}   = 90[/tex]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 ticketsHence, the total number of ticket booked altogether for students and adults is 90 + 36 =126.