Question 40·Easy·Linear Equations in Two Variables
During a fundraiser, a club sold standard raffle tickets for $3 each and premium raffle tickets for $7 each, collecting a total of $148. Which equation represents this situation if is the number of standard tickets sold and is the number of premium tickets sold?
For word problems that ask for an equation, first identify what each variable stands for, then translate each part of the situation into algebra: multiply counts by prices or rates to get expressions in dollars, and finally combine those expressions to match the total given. Pay close attention to whether quantities should be added or subtracted and make sure the coefficients (the numbers in front of variables) correctly match the prices or rates described in the problem.
Hints
Connect ticket counts to money
If each standard ticket costs $3 and there are standard tickets, what expression represents the money from standard tickets?
Do the same for premium tickets
If each premium ticket costs $7 and there are premium tickets, what expression represents the money from premium tickets?
Relate the expressions to the total
The total money collected is the sum of the money from standard tickets and premium tickets. How can you write an equation where that sum equals 148?
Desmos Guide
Represent each ticket type's revenue
In Desmos, type 3*x to represent the money from standard tickets and 7*y to represent the money from premium tickets. These expressions correspond to the revenue from each ticket type.
Form the total revenue expression
Add the two expressions in Desmos as 3*x + 7*y to represent the total money collected from both ticket types together.
Compare with the answer choices
Look at the left-hand sides of the answer choices and see which one has the same structure as the total revenue expression you built in Desmos, and which sets that total equal to 148 dollars.
Step-by-step Explanation
Translate what x and y mean
The problem tells you that:
- is the number of standard tickets sold.
- is the number of premium tickets sold.
So and count tickets, not dollars.
Write an expression for money from each type of ticket
Each standard ticket costs $3, and there are of them, so the money from standard tickets is dollars.
Each premium ticket costs $7, and there are of them, so the money from premium tickets is dollars.
Combine the parts and set equal to the total
All the money collected comes from standard tickets plus premium tickets. So the total money is the sum of the two expressions:
- Money from standard tickets:
- Money from premium tickets:
Their sum must equal the total of $148:
This matches choice D, so is the correct equation.