Question

Thirty students bought pennants for the football game. Plain pennants cost $4 each and fancy ones cost $8 each. If the total bill was $168, how many students bought the fancy pennants?

Answer 1

12 students.

Explanation:

Since the cost for the pennants' LCD is `4`, we could divide the total bill by it and see how big the bill would be in terms of plain pennants only. So...
`($168)/($4)=42`.
`$168` is the same as `42` plain pennants. Since a fancy pennant only costs two times more, we can just subtract the number of plain pennants you could buy with the money with the number of students to get the number of students who got fancy pennants`.^1` So...
`42-30=12`. 12 students bought a fancy pennant.

Footnote 1: That is so because if a student had bought a fancy pennant, he would have been counted twice in the number of plain pennants because fancy pennants cost two times more. By subtracting the actual number of students from that number, we can see how many students have been double counted, and that would be the number of fancy pennants bought.