Middle School Math Quiz: Solving Systems By Graphing
1 questions · exam conditions
0:00
Solving Systems By GraphingQuestion 1 of 1

A local theater sells adult tickets for $12 each and student tickets for $8 each. For a particular show, they need to sell exactly 100 tickets and collect exactly $1000 in revenue.

If this situation is modeled as a system of equations and graphed, what does the intersection point represent in this real-world context?

The theater sells 50 adult tickets and 50 student tickets for maximum profit
The theater sells 25 adult tickets and 75 student tickets to meet both constraints
The theater sells 40 adult tickets and 60 student tickets to satisfy the revenue requirement
The theater sells 50 adult tickets and 50 student tickets to meet both the ticket count and revenue requirements
← Back to quizzes

Middle School Math Quiz

Middle School Math Quiz: Solving Systems By Graphing

Practice Solving Systems By Graphing in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Solving Systems By Graphing, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A local theater sells adult tickets for $12 each and student tickets for $8 each. For a particular show, they need to sell exactly 100 tickets and collect exactly $1000 in revenue.

If this situation is modeled as a system of equations and graphed, what does the intersection point represent in this real-world context?

  1. The theater sells 50 adult tickets and 50 student tickets for maximum profit
  2. The theater sells 25 adult tickets and 75 student tickets to meet both constraints
  3. The theater sells 40 adult tickets and 60 student tickets to satisfy the revenue requirement
  4. The theater sells 50 adult tickets and 50 student tickets to meet both the ticket count and revenue requirements (correct answer)
Explanation: The system is: a + s = 100 (total tickets) and 12a + 8s = 1000 (total revenue), where a = adult tickets and s = student tickets. Solving: from the first equation, s = 100 - a. Substituting: 12a + 8(100 - a) = 1000, so 12a + 800 - 8a = 1000, giving 4a = 200, so a = 50 and s = 50. Verification: 50 + 50 = 100 tickets ✓ and 12(50) + 8(50) = 600 + 400 = 1000 ✓. The intersection represents the unique combination that satisfies both constraints simultaneously. Choice A mentions profit maximization which isn't specified. Choices B and C give incorrect ticket combinations.