At a seminar tickets were sold at 3 different prices student

At a seminar tickets were sold at 3 different prices: students $4 college students $9, and adults not in college $12. The number of to college school students. The number of high school students than the number of adults. a total of 38 people attended the seminar. Set up a 3 times 3 system for this problem. (an equation does b) How many high school students, college students, and adults not in college attended t seminar? How much money was collected from ticket sales?

Solution

Let the number of high school students, college students and the adults not in college be x, y and z respectively.

The number of college students was double the high school students so that y = 2x or, 2x - y = 0...(1)

The number of high school students was 2 less than the number of adults so that x = z -2 or, x - z = -2...(2)

The total number of people who attended the seminar is 38 so that x + y + z = 38... (3) On substituting y = 2x in 3rd equation, we get x + 2x + z = 38 or, 3x + z = 38...(4) Now, on adding the 2nd and 4th equations, we get x - z + 3x + z = -2 + 38 or, 4x = 36 so that x = 9. Then, from the 1st equation, y = 2x = 2*9 = 18 and from the 3rd equation, z = x + 2 = 9 + 2 = 11. We can verify the result by substituting these values of x, y, z in the 3rd equation. Thus, the number of high school students was 9, the number of college students was18 and the number adults not in college is 11.