Question 1·Easy·Linear Equations in Two Variables
A zoological park sells two types of admission passes. An adult pass costs $20, and a child pass costs $12. One family spent a total of $104 on passes and bought exactly 2 child passes. How many adult passes did the family buy?
For word problems about ticket or pass sales, start by defining a variable for the unknown quantity, then write a total-cost equation by multiplying each type of item by its price and adding them. Substitute any known quantities (like the exact number of child passes), simplify the equation, and solve step by step (combine, subtract, then divide). Finally, check that your solution makes sense in the context (non-negative whole number of items) and matches one of the answer choices.
Hints
Translate the words into an equation
Try to write an equation for the total cost of all the passes using a variable for the number of adult passes.
Use the information about child passes
The family bought exactly 2 child passes. How much did those 2 child passes cost altogether, and how can you include that in your equation?
Isolate the variable step by step
Once you have an equation with your variable and numbers, first combine like terms, then move the constant term to the other side, and finally divide to solve for the variable.
Desmos Guide
Use Desmos to compute the number of adult passes
In Desmos, type the expression (104 - 12*2) / 20 and press Enter. The value that Desmos outputs is the number of adult passes the family bought.
Step-by-step Explanation
Define the variable
Let represent the number of adult passes the family bought.
We are told:
- Each adult pass costs $20.
- Each child pass costs $12.
- The family bought 2 child passes.
- The total cost was $104.
Write an equation for the total cost
Write an expression for the total amount of money spent.
- Cost of adult passes: (because each adult pass is $20 and there are of them).
- Cost of child passes: .
So the total cost equation is:
Simplify and solve for the number of adult passes
First, simplify the child-pass part:
So the equation becomes:
Subtract 24 from both sides:
Now divide both sides by 20:
Interpret the solution and choose the answer
Compute the division:
So the family bought 4 adult passes. Among the choices given, this corresponds to answer choice B) 4.