# algebra

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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?

• algebra -

By system of equations:
C=number of child 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 (260-150)/10=11 adults.
So there were 11 adults and 14 children.

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