A one-variable model works when two groups share a fixed total: count one group with a letter, then write the other as what’s left. Multiply each count by its ticket price to get the money from that group. The phrase more than calls for the difference between those amounts. Adding them instead would model total money collected.
Hints
- Hint 1
The two ticket counts make a fixed total. If tickets are orchestra tickets, the remaining tickets must be balcony tickets. What expression counts the remainder out of ?
- Hint 2
A ticket price is dollars per ticket. Multiply each price by its own ticket count to get that group’s revenue, or money collected. Which count goes with the $18 price?
- Hint 3
The words more than compare two amounts of money. Subtract the balcony revenue from the orchestra revenue to express how much more the orchestra tickets brought in. Is $1,080 a difference or a combined total?
Step-by-step
Build the two revenues, then compare them
Step 1Count the balcony tickets
No Desmos needed. You’re building an equation from the story, not solving one. Since counts orchestra tickets out of total, the balcony tickets are the rest:
- Step 2
Write each group’s revenue
Revenue means money collected. Multiply each price by its own ticket count:
Using for balcony revenue would count tickets in both groups.
- Step 3
Set the difference equal to $1,080
“More than” means subtract the balcony revenue from the orchestra revenue, not add them. That difference is $1,080, so:
This equation can be used to find , the number of orchestra tickets sold. Choice D.