Since there are two unknowns, we need two equations to solve the problem. Since there are no equations written out for us, they must be implied in the wording of question.
The first two sentences contain the first equation. We know from the first sentence, “A total of 369 tickets were sold...” how many tickets there are and from the second sentence “they were adult tickets or students tickets” that there are only two types of ticket. All the tickets (369) must be adult tickets or student tickets. We can now write our first equation
Equations (1) 369 = A + S
A is the number of adult tickets and S the number of student tickets.
The third sentence “the number of student tickets sold was two times the number of adult tickets sold...” tells us the second equation. The key to this sentence is the verb “was.” To be verbs like “is,” “was,” or “will be” in math equations can be represented using the “=” sign. Therefore the second equation is:
(2) S = 2A
Again the first equation was:
(1) 369 = A + S
To solve this problem we now use substitution by plugging in for S in equation (1) using the idea that S = 2A from equation (2). The first equation is now.
369 = A + 2A
Which simplifies to
369 = 3A
After we divide both sides by 3, we are left with
123 = A
which is the number of adult tickets sold.
