Question
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Serena makes \( \$ 9 \) per hour cutting lawns. Each day, she earns about \( \$ 15 \) in tips. If Serena made no less than \( \$ 110 \) on Monday, which inequality represents \( h \), the number of hours she worked on Monday? \( \begin{array}{l}15 h+9 \leq 110 \\ 15 h+9 \geq 110 \\ 9 h+15 \geq 110 \\ 9 h+15<110\end{array} \)

Ask by Donnelly Floyd. in the United States
Jan 30,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The correct inequality is \( 9h + 15 \geq 110 \).

Solution

To determine the correct inequality representing the number of hours \( h \) Serena worked on Monday, let's break down her earnings: 1. **Hourly Earnings:** - Serena earns \$9 per hour. - For \( h \) hours, she earns \( 9h \) dollars. 2. **Daily Tips:** - She earns a fixed \$15 in tips each day. 3. **Total Earnings:** - Her total earnings for the day are the sum of her hourly earnings and tips: \[ \text{Total Earnings} = 9h + 15 \] 4. **Minimum Earnings Constraint:** - Serena made **no less than** \$110 on Monday. This means her total earnings are **greater than or equal to** \$110. - This can be expressed as: \[ 9h + 15 \geq 110 \] Among the given options, the third one correctly represents this relationship. **Answer:** \( 9 h+15 \geq 110 \)

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Bonus Knowledge

To find the correct inequality representing the situation, we can break it down: Serena earns \( 9h \) dollars from cutting lawns, and she also earns \( 15 \) dollars in tips. The total earnings must be no less than \( 110 \), which translates to the equation: \[ 9h + 15 \geq 110. \] So, the correct answer is: \( 9h + 15 \geq 110. \) Here's a fun fact: This situation translates to a classic "earnings problem" often used in algebra classes to teach inequalities. The concept of combining base earnings with variable factors like tips or bonuses makes it relatable and a handy way to understand inequalities in real life! Additionally, when solving this inequality, you might find it helpful to isolate \( h \). First, subtract 15 from both sides, which gives you \( 9h \geq 95 \). Then divide by 9 to find the minimum hours Serena needs to work for her desired earnings. Neat, right?

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