A fixed number of one type of pass and a total cost leave a one-variable equation, an equation with only one unknown count. Multiply each price by its pass count, then add the costs to match the total. Solve the equation with a Desmos regression. The fixed pass count doesn’t get multiplied by the unknown count.
Hints
- Hint 1
A variable is a letter for the count you don’t know. Call the adult count . At $20 per adult, what expression gives the cost of all the adult passes?
- Hint 2
The child count is fixed at , so its cost doesn’t change with the adult count. Find the child cost, then add it to the adult cost to match the total.
- Hint 3
A Desmos regression uses to find a number that makes both sides match. Replace the adult-count letter with so Desmos solves for it instead of graphing it.
Step-by-step
Write one cost equation
Step 1Find the child-pass cost
The family bought exactly 2 child passes at $12 each, so they cost dollars. That cost stays fixed, no matter how many adult passes the family bought.
- Step 2
Match the costs to the total
Let be the number of adult passes. At $20 each, they cost . Price times count gives each part of the total. Add the $24 child cost to match the $104 spent:
- Step 3
Solve for the adult count
Type in Desmos. Use in place of and in place of so Desmos finds the value that makes the costs match. Under PARAMETERS, it shows . Since counts adult passes, the family bought 4 adult passes. Choice B.