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Real-World Inequalities Practice
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Real-World Inequalities Practice
Write an inequality for each situation. Show your working when solving, and use the number lines where requested.
Formulating Inequalities
1.A community theatre has $168 available for tickets priced at $21 each. Let t be the number of tickets it can buy. Write an inequality to model the budget.
2.A courier has at most 7 hours for a route. Loading takes 35 minutes, and each stop takes 20 minutes. If d is the number of stops, write an inequality using minutes.
3.A hiking pack can weigh no more than 18 kg. The empty pack weighs 2.8 kg. Let w be the weight, in kilograms, of the gear packed inside. Write an inequality for w.
4.A streaming plan costs $19 per month, plus $0.80 for each movie rental. A customer wants to spend no more than $35 in total. If r is the number of rentals, write an inequality.
Solving and Graphing
5.Solve the ticket-budget inequality from the first section. Give the greatest whole-number value of t, then show the solution on the number line.
6.A rideshare fare has a $5.20 starting charge and costs $1.80 per kilometre. With a spending limit of $32, solve 5.20 + 1.80k ≤ 32 to find the maximum distance k, in kilometres.
7.A reptile enclosure should stay between 19°C and 27°C, including both limits. Let T be its temperature. Write a compound inequality and graph the acceptable temperatures.
Extension Challenge
8.A community fundraiser sells meal tickets for $28 each. The hall hire costs $260, and each meal costs $11. The hall can seat at most 95 people. To make a profit of at least $900, how many tickets must be sold? Write and solve an inequality, then give the possible whole-number ticket range.
9.A school club has $240 to buy reusable drink bottles costing $16 each. Let b be the number of bottles. Write an inequality, solve it, and state the greatest number of bottles the club can buy.
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