Question 22·Easy·Linear Equations in Two Variables
At a carnival, child tickets cost $4 each and adult tickets cost $12 each. The total amount collected from 8 child tickets and a certain number of adult tickets was $104. How many adult tickets were sold?
For word problems about tickets or prices, translate the situation into arithmetic or an equation: multiply each known quantity by its price, subtract known parts from the total to isolate the unknown part, then divide by the appropriate unit price. Always check by plugging your result back into the original context (here, recomputing the total money) to make sure it matches the given total.
Hints
Start with the known child tickets
You know there were 8 child tickets at $4 each. How much money is that in total?
Separate child and adult money
Once you know how much money came from child tickets, subtract that from the total $104 to see how much came from adult tickets.
Use the adult ticket price
You will know how many dollars came from adult tickets and that each adult ticket is $12. What operation will give you the number of adult tickets?
Desmos Guide
Use Desmos to compute the number of adult tickets
In the expression line, type (104 - 4*8) / 12 and press Enter. The value that Desmos outputs is the number of adult tickets sold.
Step-by-step Explanation
Find the total cost of the child tickets
Each child ticket costs $4, and there are 8 child tickets.
So the total cost for children is
This means $32 is from child tickets.
Find how much money came from adult tickets
The total money collected was $104, and $32 of that was from child tickets.
Subtract to find the amount from adult tickets:
So $72 came from adult tickets.
Use the adult ticket price to find the number of adult tickets
Each adult ticket costs $12, and the total from adult tickets is $72.
Divide to find the number of adult tickets:
So, the number of adult tickets sold was 6.