A music venue models the revenue , in dollars, from selling tickets to a concert as
If the venue can seat no more than 25 people, how many tickets must be sold for the revenue to equal $1,200?
A quadratic model can produce the same revenue at two different ticket counts. Set the model equal to the target revenue, then graph both sides in Desmos to find those counts. Apply the seat limit to the ticket count, not the revenue. Selling every available seat isn't automatically necessary to reach a target.
Hints
- Hint 1
The output is revenue, while the input counts tickets. To find the ticket count for a given revenue, set equal to the target. What equation does that give?
- Hint 2
The domain is the set of inputs that make sense in the situation. Since counts tickets, it must be a whole number from through the seat limit.
- Hint 3
A quadratic graph can meet a horizontal target line twice. Graph the revenue and the target on separate lines, then click both intersections. Which -coordinate fits the venue's capacity?
Step-by-step
Graph the target revenue, then check capacity
Step 1Match the revenue to the target
is the output in dollars. The requested revenue is $1,200, so write:
- Step 2
Limit the ticket count
The domain is the set of possible inputs. Since counts tickets and the venue has no more than seats, must be a whole number in this range:
The limit applies to tickets, not dollars.
- Step 3
Read both crossings and choose the allowed count
Type and on separate lines. Click both intersections, where the graphs show the same revenue. Desmos shows and . The first coordinate counts tickets; exceeds the -seat limit. So the venue must sell tickets to make $1,200. Choice B.