Math Bell Ringer for Grades 9–12: Solving a ticket-sales system of equations
A free math bell ringer for grades 9–12. Put the prompt on the board as students walk in, give them three to five minutes, then go over it together. The answer and teacher notes are in the box below the prompt.
The prompt
A theater sold 150 tickets for a play and collected $1,350. Adult tickets cost $12 and student tickets cost $7. Write a system of equations and solve it to find how many of each ticket were sold.
Answer and teacher notes
Let a = adult tickets and s = student tickets.
a + s = 150
12a + 7s = 1,350
Substitute s = 150 − a: 12a + 7(150 − a) = 1,350 → 12a + 1,050 − 7a = 1,350 → 5a = 300 → a = 60 adult tickets, so s = 90 student tickets.
Check: 60 + 90 = 150 tickets, and 60 × $12 + 90 × $7 = $720 + $630 = $1,350. Fast estimate for discussion: if all 150 were student tickets, the total would be $1,050; each adult ticket adds $5, and $300 ÷ $5 = 60 adults.
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