What you’ll learn
Model real situations with systems.
Key idea
A count total adds counts; a revenue total adds each count multiplied by its own category price.
Match count and dollar units; each variable retains its own price coefficient, with distinct prices ensuring a unique feasible pair.
Worked example
Enter the exact value or ordered values in the format requested below.
A show sells adult tickets at $8 and child tickets at $3; 10 tickets yield $40. Let x count adults and y count children. Write both modeling equations separated by a semicolon; no solution is required.
- x and y count adult and child tickets; their unweighted sum is x+y=10.
- Multiplying each category by its own dollar price gives 8x+3y=40; both count and money equations are needed.
Answer: x+y=10;8x+3y=40
Quick Check
Choose which candidate representation satisfies the requirements of 'Model real situations with systems' and justify the choice.
A show sells adult tickets at $8 and child tickets at $3; 7 tickets yield $51. Let x count adults and y count children. Select the system satisfying both constraints and justify the units.