Students can practice setting up and solving inequalities using these real-life math scenarios involving savings, travel costs, and grades.

Let's solve each of the inequality word problems step by step and explain the reasoning.

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Problem 1: Sara’s Savings

Problem:
Sara goes to Fredonia University. She has $900 in her savings account. She needs to buy a small laptop computer before the next semester. The laptop costs $600. Every 2 weeks she withdraws $60 from her savings account for food. How many times can Sara withdraw money for food? Write an inequality to explain.

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#### Step-by-step Solution:

1. Initial amount in savings: $900
2. Cost of laptop: $600
3. Amount left after buying laptop:
$$
900 - 600 = 300
$$
So, Sara has $300 left to use for food withdrawals.

4. Each withdrawal: $60 every 2 weeks
Let $ x $ = number of times she can withdraw $60 for food.

5. Total spent on food: $60x

6. She cannot spend more than $300:
$$
60x \leq 300
$$

7. Solve the inequality:
$$
x \leq \frac{300}{60} = 5
$$

So, Sara can withdraw money for food up to 5 times.

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✔ Answer:
Inequality: $ 60x \leq 300 $
Sara can withdraw money for food 5 times.

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Problem 2: Limo Rental

Problem:
You want to rent a limousine for a trip to the city. The limo costs $700 for the night and $0.15 per mile. You have $750 to spend. Write an inequality that represents this scenario. How many miles can the limo travel?

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#### Step-by-step Solution:

1. Fixed cost (for the night): $700
2. Variable cost: $0.15 per mile
Let $ m $ = number of miles traveled

3. Total cost:
$$
700 + 0.15m
$$

4. Maximum budget: $750
So:
$$
700 + 0.15m \leq 750
$$

5. Solve the inequality:
Subtract 700 from both sides:
$$
0.15m \leq 50
$$

Divide both sides by 0.15:
$$
m \leq \frac{50}{0.15} = \frac{5000}{15} = 333.\overline{3}
$$

Since you can't travel a fraction of a mile in practical terms (and we're dealing with a real-world limit), the maximum whole number of miles is 333 miles.

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✔ Answer:
Inequality: $ 700 + 0.15m \leq 750 $
The limo can travel up to 333 miles.

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Problem 3: Jessica’s Math Grade

Problem:
Jessica is getting ready for college. She needs to have an overall grade of 85 in her Math class to qualify for the college that she wished to attend. Her math grade is based solely on her scores on 6 exams. On the first 5 exams her scores were 87, 81, 85, 90, 78. Write an inequality that represents her predicament. What score does she need to get on her last test to qualify?

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#### Step-by-step Solution:

1. She needs an average of at least 85 over 6 exams.
Let $ x $ = score on the 6th (last) exam.

2. Sum of first 5 exam scores:
$$
87 + 81 + 85 + 90 + 78 = 421
$$

3. Total sum of all 6 exams: $ 421 + x $

4. Average:
$$
\frac{421 + x}{6} \geq 85
$$

5. Solve the inequality:
Multiply both sides by 6:
$$
421 + x \geq 510
$$

Subtract 421:
$$
x \geq 510 - 421 = 89
$$

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✔ Answer:
Inequality: $ \frac{421 + x}{6} \geq 85 $
Jessica needs to score at least 89 on her last test to qualify.

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✔ Final Answers Summary:

1. Sara:
Inequality: $ 60x \leq 300 $ → $ x \leq 5 $
She can withdraw 5 times.

2. Limo:
Inequality: $ 700 + 0.15m \leq 750 $ → $ m \leq 333.\overline{3} $
Maximum 333 miles.

3. Jessica:
Inequality: $ \frac{421 + x}{6} \geq 85 $ → $ x \geq 89 $
She needs at least 89 on the last test.

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Let me know if you'd like these formatted as a printable solution sheet!