What you’ll learn
Create systems from constraints.
Key idea
One equation counts all tickets; another totals dollars using each category's own price.
Ticket and dollar totals belong to separate equations; attach each price to its own category and preserve both constraints.
Worked example
Enter the exact value or ordered values in the format requested below.
Theater adult tickets cost 9 dollars,child tickets 4; x=adult count,y=child count. Exactly 5 tickets yield 35 dollars. Create two equations separated by a semicolon; do not solve.
- Counts give x+y=5; category price times count gives 9x+4y=35.
- Both labeled constraints form x+y=5;9x+4y=35; feasible counts x=3,y=2 verify the totals, but the task asks for the full system, not only its solution.
Answer: x+y=5;9x+4y=35
Quick Check
Choose which candidate representation satisfies the requirements of 'Create systems from constraints' and justify the choice.
Theater adult tickets cost 9 dollars,child tickets 6; x=adult count,y=child count. Exactly 7 tickets yield 51 dollars. Labeled price/count table rows adult (9,x),child (6,y), margins tickets 7,dollars 51. Select the complete model.