Question

A theme park charges 10 for adults and 5 for kids. How many kids tickets were sold if a total of 548 tickets were sold for a total of $3750? 
 

• A. 431
• B. 157
• C. 346
• D. 248
• E. 269

Hint:

A useful check for this type of problem is to calculate the 'average' ticket price. $3750 / 548 tickets \(\approx\) $6.84. Since this is closer to the kids' price ($5) than the adult price ($10), you should expect there to be more kids tickets than adult tickets. 346 kids tickets and (548 - 346) = 202 adult tickets fits this expectation.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem can be modeled by a system of two linear equations with two variables. One equation represents the total number of tickets, and the other represents the total revenue.
Step 2: Key Formula or Approach:
Let \(a\) be the number of adult tickets and \(k\) be the number of kids tickets.
Equation 1 (Total tickets): \(a + k = 548\)
Equation 2 (Total revenue): \(10a + 5k = 3750\)
We need to solve this system for \(k\).
Step 3: Detailed Explanation:
We can use the substitution method. From Equation 1, we can express \(a\) in terms of \(k\): \[ a = 548 - k \] Now, substitute this expression for \(a\) into Equation 2: \[ 10(548 - k) + 5k = 3750 \] Distribute the 10: \[ 5480 - 10k + 5k = 3750 \] Combine the k terms: \[ 5480 - 5k = 3750 \] Now, we want to isolate k. Subtract 3750 from both sides and add 5k to both sides: \[ 5480 - 3750 = 5k \] \[ 1730 = 5k \] Finally, divide by 5 to find k: \[ k = \frac{1730}{5} \] \[ k = 346 \] Step 4: Final Answer:
The number of kids tickets sold was 346.