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This problem involves a system of linear equations. We are given the following details:

- The number of total tickets sold: 172
- The total sales amount: \$1212.40
- The child ticket price: \$5.50
- The adult ticket price: \$9.10

Let:
- $ x $ be the number of adult tickets sold.
- $ y $ be the number of child tickets sold.

We can set up the system of equations:

1. $ x + y = 172 $  (because the total number of tickets sold is 172)
2. $ 9.10x + 5.50y = 1212.40 $  (the total sales equation based on the prices of adult and child tickets)

### Solving this system of equations:

From the first equation:
\[ y = 172 - x \]

Substitute this into the second equation:
\[
9.10x + 5.50(172 - x) = 1212.40
\]

Now I'll solve for $ x $, the number of adult tickets.The number of adult tickets sold that day is 74.

Would you like any further details or explanations?

Here are some related questions to expand your understanding:
1. How many child tickets were sold that day?
2. How would the solution change if the total sales were different but the prices remained the same?
3. How can systems of linear equations be applied to other real-life scenarios?
4. What methods are available to solve systems of linear equations, and how do they compare?
5. How would rounding affect the solution in this case if the ticket prices were non-integer values?

**Tip:** When solving systems of equations, substitution and elimination methods are often the simplest to apply for two-variable problems.

At the city museum, child admission is $5.50 and adult admission is $9.10. On Thursday, 172 tickets were sold for a total sales of $1212.40. How many adult tickets were sold that day?

Solve a system of linear equations to find how many adult tickets were sold at a museum. The total tickets sold were 172, with adult tickets priced at $9.10 and child tickets at $5.50, resulting in total sales of $1212.40.

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