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

$$
LATEXBLOCK0
$$

Translate the first scenario

Using the System of Equations Translation knowledge point

$$ 12a + 5c = 169 $$

Translate the second scenario

Using the System of Equations Translation knowledge point

$$ 22a + 10c = 314 $$

Combine into a system

Using the System of Equations knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) \(12a + 5c = 314\)

\(22a + 10c = 169\)

• **(B) \(12a + 5c = 169\)

\(22a + 10c = 314\) (Correct answer)**

• (C) \(5a + 12c = 314\)

\(22a + 10c = 169\)

• (D) \(22a + 5c = 169\)

\(12a + 10c = 314\)