Question 76·Easy·Linear Equations in Two Variables
A community theater sold two types of tickets for a weekend performance. The theater’s ticket revenue totaled $3,200. The equation models this situation, where is the number of adult tickets sold and is the number of child tickets sold.
According to the equation, which of the following represents the price, in dollars, of each child ticket?
For revenue word problems modeled by linear equations, first match each variable to what it counts (like number of adult or child tickets). Then recognize that each term in the equation is (price per item) × (number of items), so the coefficient (number in front) of each variable is the per-item price. Focus on the term that includes the variable mentioned in the question and choose the answer that shows just that coefficient, not a product involving the variable or the total revenue.
Hints
Connect the equation to the word problem
Think about how you usually calculate total ticket revenue: you do (price per ticket) × (number of tickets) and then add the amounts for each type of ticket.
Identify the role of and
is the number of adult tickets and is the number of child tickets. Which parts of the equation must then represent the money from adult tickets and from child tickets?
Look at the term with
Find the term that includes in the equation. In that term, which part is the number of child tickets and which part is the price per child ticket?
Match to the answer choices
Once you know which part of the equation is the price per child ticket, check which answer choice shows just that price, not the total money or a product with a variable.
Desmos Guide
Enter the equation
Type 12a + 8c = 3200 into Desmos. Notice that the letters and are treated as variables and the numbers next to them are multiplying those variables.
Identify the child ticket price from the equation
Look at the term that contains in the equation you entered. The plain number (coefficient) attached to is the price of one child ticket; compare that number to the answer choices.
Step-by-step Explanation
Understand what each part of the equation means
The equation represents total revenue.
- is the number of adult tickets.
- is the number of child tickets.
- Each term (like ) is (price per ticket) × (number of tickets).
Match terms to ticket types
The term with , which is , must represent the money from adult tickets. So the number multiplying is the price of one adult ticket.
Similarly, the term with must represent the money from child tickets, so the number multiplying is the price of one child ticket.
Focus on the child ticket term
Look specifically at the term that involves , which represents child tickets. In that term, the price per child ticket is the constant factor (the plain number) that is multiplied by .
Identify the child ticket price and match it to a choice
In the equation , the term with is , so the constant factor multiplying is 8. That means each child ticket costs 8 dollars, which corresponds to answer choice B) 8.