Question

mary used the equation \\(296 = 5h + 186\\) to determine her salary at the restaurant last week. which situation does this equation best represent?

a. mary worked 5 hours at the restaurant last week. she took home her regular earnings of \\$186 plus tips for a total of \\$296. how much were her tips, \\(h\\)?

b. mary earns \\$5 per hour as a waitress. last week she took home her regular earnings of \\$296 plus \\$186 in tips. how many hours, \\(h\\), did she work last week?

c. mary earns \\$296 per week as a waitress. last week she took home her regular earnings of \\$186 plus \\$5 in tips. how many hours, \\(h\\), did she work last week?

d. mary earns \\$5 per hour as a waitress. last week she took home her regular earnings of \\$5 per hour plus \\$186 in tips for a total of \\$296. how many hours, \\(h\\), did she work last week?

Explanation:

Analyze the given equation

The given equation is:

$$296 = 5h + 186$$

Interpret each term in the equation

• \(296\): The total amount earned (total salary).
• \(5h\): The hourly earnings, where \(5\) represents the hourly rate of \(\$5\) per hour, and \(h\) represents the number of hours worked.
• \(186\): A constant amount, representing fixed earnings or tips of \(\$186\).

Match with the given options

• Option A: Says she worked \(5\) hours and tips are \(h\). This would be modeled by \(296 = 5 \times \text{rate} + 186\), which does not match.
• Option B: Says regular earnings are \(\$296\) plus \(\$186\) in tips, which does not match the structure.
• Option C: Says she earns \(\$296\) per week, which does not match.
• Option D: Says she earns \(\$5\) per hour (represented by \(5h\)) plus \(\$186\) in tips for a total of \(\$296\). This perfectly matches \(296 = 5h + 186\), where \(h\) is the number of hours worked.

Answer:

• (A) Mary worked 5 hours at the restaurant last week. She took home her regular earnings of $186 plus tips for a total of $296. How much were her tips, h?
• (B) Mary earns $5 per hour as a waitress. Last week she took home her regular earnings of $296 plus $186 in tips. How many hours, h, did she work last week?
• (C) Mary earns $296 per week as a waitress. Last week she took home her regular earnings of $186 plus $5 in tips. How many hours, h, did she work last week?
• (D) Mary earns $5 per hour as a waitress. Last week she took home her regular earnings of $5 per hour plus $186 in tips for a total of $296. How many hours, h, did she work last week? (Correct answer)