SAT Linear Systems: Solve an Adult and Student Ticket Problem

A school event sells 38 tickets. Adult tickets cost $12 each, and student tickets cost $7 each. Total ticket revenue is $356. How many adult tickets were sold?

Represent both totals

Let a be adult tickets and s be student tickets. The number of tickets gives a + s = 38. Revenue gives 12a + 7s = 356.

Eliminate one variable

Multiply a + s = 38 by 7 to obtain 7a + 7s = 266. Subtract it from the revenue equation: 5a = 90, so a = 18.

Check in the original situation

Then s = 20. The counts total 38, and 12(18) + 7(20) = 216 + 140 = 356.

Treat every ticket as a $7 student ticket. That would raise $266. Each adult ticket adds $5, so the extra $90 requires 90/5 = 18 adult tickets. This is elimination expressed through the context.

• 14 adults would produce $336, below the stated revenue.
• 20 is the student count. The question asks for adults.
• 24 adults would produce $386, above the stated revenue.

An event sells 25 tickets at $10 for adults and $6 for students, for a total of $198. How many adult tickets were sold?

Answer: 12

All student tickets would raise 25 × 6 = 150. The remaining 48 dollars divided by the 4-dollar adult premium gives 12 adults; 12(10) + 13(6) = 198.

If this was difficult, return to linear systems practice and identify the precise step to improve. These are original PeakSAT teaching examples, not official College Board questions or calibrated score predictions. For official adaptive test practice, use Bluebook (opens in a new tab).