MATH SOLVE

4 months ago

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.