Question

a high school drama club is selling tickets for the spring production. one day the president sold 12 adult tickets and 5 child tickets for a total of $169. the next day the president sold 22 adult tickets and 10 child tickets for a total of $314. let a represent the cost of one adult ticket. let c represent the cost of one child ticket. which system of equations will solve for a and c?

\\(12a + 5c = 314\\)
\\(22a + 10c = 169\\)

\\(12a + 5c = 169\\)
\\(22a + 10c = 314\\)

\\(5a + 12c = 314\\)
\\(22a + 10c = 169\\)

\\(22a + 5c = 169\\)
\\(12a + 10c = 314\\)

Explanation:

Identify the variables

Using the Variable Identification knowledge point

• Let \(a\) represent the cost of one adult ticket.
• Let \(c\) represent the cost of one child ticket.

Translate the first day's sales

Using the Algebraic Translation knowledge point

• The president sold 12 adult tickets and 5 child tickets for a total of \$169.
• This translates to the equation:

$$12a + 5c = 169$$

Translate the second day's sales

Using the System of Equations Translation knowledge point

• The next day, the president sold 22 adult tickets and 10 child tickets for a total of \$314.
• This translates to the equation:

$$22a + 10c = 314$$

Formulate the system of equations

Using the System of Equations knowledge point

• Combining both equations gives the system:

$$
LATEXBLOCK0
$$

Answer:

• (A) \(12a + 5c = 314\) and \(22a + 10c = 169\)
• (B) \(12a + 5c = 169\) and \(22a + 10c = 314\) (Correct answer)
• (C) \(5a + 12c = 314\) and \(22a + 10c = 169\)
• (D) \(22a + 5c = 169\) and \(12a + 10c = 314\)