Sure! Here are five word problems that involve inequalities:
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Concert Tickets: A concert venue has a seating capacity of 5,000. If 1,200 tickets have already been sold, how many more tickets can be sold without exceeding the venue's capacity? Write an inequality to represent the situation.
Inequality: \( x + 1200 \leq 5000 \)
Solution: \( x \leq 3800 \) -
Study Hours: Maria needs to study at least 15 hours this week to prepare for her exams. If she has already studied for 7 hours, how many more hours does she need to study to meet her goal? Write an inequality to represent the situation.
Inequality: \( 7 + x \geq 15 \)
Solution: \( x \geq 8 \) -
Budgeting for a Party: Jake is planning a party and has a budget of $200. He has already spent $75 on decorations. If he wants to spend no more than his budget on food and drinks, how much can he spend? Write an inequality to represent the situation.
Inequality: \( 75 + x \leq 200 \)
Solution: \( x \leq 125 \) -
Running Distance: Lydia is training for a marathon and aims to run at least 30 miles per week. If she has already run 18 miles this week, how many more miles does she need to run? Write an inequality to represent the situation.
Inequality: \( 18 + x \geq 30 \)
Solution: \( x \geq 12 \) -
Saving for a Trip: Tom wants to save at least $1,000 for a trip. He currently has $450 saved. If he plans to save $50 each week, how many weeks will it take to reach his goal? Write an inequality to represent the situation.
Inequality: \( 450 + 50x \geq 1000 \)
Solution: \( x \geq 11 \)
Feel free to use, modify, or expand upon these problems as you see fit!
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