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s: number of students
a: number of adults


Students paid 2 × s dollars and adults paid 3 × a dollars. They totaly paid $1050


2s + 3a = 1050

the sum of number of students and adults is given as 400


s + a = 400


Seems like a systems of linear equations question:


2s + 3a = 1050
s + a = 400


Multiply both sides of second equation with -2

2s + 3a = 1050
-2 × (s + a) = -2 × (400)


Add each sides of the equations:


2s + 3a = 1050
-2s - 2a = -800
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a = 1050 -800 = 250 (number of adults)


Let's take the sum of the attendees equation:


s + a = 400


Let's plug the number of adults in the equation:


s + 250 = 400


(s + 250) -250 = (400) -250


s = 150 (number of students)


August 25, 2008, 7:33 pm

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