Question

​There is a total of 360 students and teachers ​​at a school.​​ A trip is organized and 65% of ​​the students and teachers bought ​​tickets to go on ​this trip.​​

(a)​ ​Work out how many ​of the students and teachers​​​ bought tickets to go on the trip​.
​The number of teachers,the number of male students and the number of female students ​​​​​who bought tickets ​​to go on the trip are in the ratios ​1:3:5 ​.
(b) ​Calculate the number of female students who bought tickets to go on the trip​​​​​.
​All the male students who bought tickets went on the trip ​​​but 4 of the female students ​​​who bought tickets did not go on the trip​​​.
(c) ​Find the ratio of the number of male students ​who went on the trip to the number of ​​female students who went on the trip​​​​.​​

Answer 1

Answer: Below :)

Explanation:

(a) The percentage of students and teachers who bought tickets to go on the trip is 65%. So the number of students and teachers who bought tickets can be found by multiplying the total number of students and teachers by 65%:

65/100 x 360 = 234

Therefore, 234 students and teachers bought tickets to go on the trip.

(b) Let the number of teachers who bought tickets be x. Then the number of male students who bought tickets is 3x, and the number of female students who bought tickets is 5x.

The total number of students and teachers who bought tickets is:

x + 3x + 5x = 9x

We know that 234 students and teachers bought tickets, so we can set up the following equation:

9x = 234

Solving for x, we get:

x = 26

So the number of teachers who bought tickets is 26, the number of male students who bought tickets is 78 (3x), and the number of female students who bought tickets is 130 (5x).

However, 4 of the female students who bought tickets did not go on the trip, so the actual number of female students who went on the trip is:

130 - 4 = 126

(c) The ratio of the number of male students who went on the trip to the number of female students who went on the trip is:

78/126

Simplifying this ratio by dividing both numerator and denominator by 6, we get:

13/21

Therefore, the ratio of the number of male students who went on the trip to the number of female students who went on the trip is 13:21.