algebra
posted by steven .
Adult tickets for a play cost $16 and child tickets cost $6. If there were 25 people at a performance and the theater collected $260 from ticket sales, how many adults and how many children attended the play?

By system of equations:
C=number of child tickets sold
A=number of adult tickets sold
C+A = 25
6C+16A = 260
Solve for A and C (by substitution).
Solving the problem in the head without pencils or paper or calculator:
Adult tickets cost $10 more than child tickets. If all 25 were child tickets, they would have gathered 6*25=$150.
To get $260, there must have been (260150)/10=11 adults.
So there were 11 adults and 14 children.