A movie theater charges $12 for each adult ticket and $8 for each child ticket. Dominic bought 5 tickets in total and spent $52. How many of the tickets Dominic bought were child tickets?
A one-variable equation fits a purchase with two ticket types, a combined count, and a total cost. Name the count the question asks for; subtract it from the total to count the other type. Multiply each count by its ticket price, then solve the cost equation with a Desmos regression. Treating the total as one group's count charges for too many tickets.
Hints
- Hint 1
Let count child tickets. Since adult and child tickets make up the total, the adult count is the total minus . What expression gives the adult count?
- Hint 2
Each ticket price is a rate in dollars per ticket. Multiply each rate by the number of tickets of that type, then set the combined cost equal to the amount Dominic spent.
- Hint 3
Once you've written the cost equation, solve it as a regression in Desmos. Replace with and with ; Desmos will report the child count under PARAMETERS.
Step-by-step
Write one cost equation
Step 1Count the adult tickets
Let count child tickets. The tickets are adults and children together, so every ticket not counted in is an adult ticket. Subtract to get the adult count: . Using for adults would put the child tickets on top of the five Dominic bought.
- Step 2
Turn the costs into an equation
At $12 each, the adults cost dollars. At $8 each, the children cost dollars. These two costs add to the $52 Dominic spent: . Both terms count dollars, not tickets.
- Step 3
Solve for child tickets in Desmos
Type . This regression uses for the unknown child count and to ask Desmos to make the two sides equal. Under PARAMETERS, Desmos shows . Since counts child tickets, Dominic bought child tickets. Grid in 2.