Activity
An elevator car in a skyscraper can hold at most 15 people. For safety reasons, each car can carry a maximum of 1,500 kg. On average, an adult weighs 70 kg and a child weighs 35 kg. Assume that each person carries 4 kg of gear with them.
Write as many equations and inequalities as you can think of to represent the constraints in this situation. Be sure to specify the meaning of any letters that you use. (Avoid using the letters , , or .)
Compare your answer: Your answer may vary, but here are some samples:
- , where represents the number of people in an elevator car.
- , where represents the number of adults and represents the number of children in an elevator car.
- , where represents the weight in kilograms in one elevator car.
After you have finished the following tasks, explain the adjustments you made to the equations and inequalities so that they are communicated more clearly.
Trade your work with a partner and read each other’s equations and inequalities.
- Explain to your partner what you think their statements mean, and listen to their explanation of yours.
- Make adjustments to your equations and inequalities so that they are communicated more clearly.
Compare your answer:
Your answers will vary.
Rewrite your equations and inequalities so that they would work for a different building where:
- an elevator car can hold at most people
- each car can carry a maximum of kilograms
- each person carries kg of gear
Compare your answer: Your answer may vary, but here are some samples.
Video: Writing Inequalities to Represent Constraints Solution
Watch the following video to further explain the solution to the activity you just completed.
Self Check
Serena is running a juice shop. Oranges cost $2 per pound. She can spend at most $64 per day on oranges. If represents the number of pounds of oranges Serena can buy per day, which of the following inequalities is true?
Additional Resources
Applications with Linear Inequalities
Many real-life situations require us to solve inequalities. The method we will use to solve applications with linear inequalities is very much like the one we used when we solved applications with equations.
We will read the problem and make sure all the words are understood. Next, we will identify what we are looking for and assign a variable to represent it. We will restate the problem in one sentence to make it easy to translate into an inequality.
Example
Dawn won a mini-grant of $4,000 to buy tablet computers for her classroom. The tablets she would like to buy cost $254.12 each, including tax and delivery. Write an inequality to represent the maximum number of tablets Dawn can buy.
Solution
Step 1 - Read the problem.
Step 2 - Identify what you are looking for. the maximum number of tablets Dawn can buy
Step 3 - Name what you are looking for.
Choose a variable to represent that quantity. Let the number of tablets.
Step 4 - Translate. Write a sentence that gives the information to find it.
$254.12 times the number of tablets is no more than $4,000. Translate into an inequality.
Try it
Try It: Applications with Linear Inequalities
Angie has $20 to spend on juice boxes for her son’s preschool picnic. Each pack of juice boxes costs $2.63. Write an inequality to represent the maximum number of packs, , she can buy.
Compare your answer:
Daniel wants to surprise his girlfriend with a birthday party at her favorite restaurant. It will cost $42.75 per person for dinner, including tip and tax. His budget for the party is $500. Write an inequality to represent the maximum number of people, , Daniel can have at the party.
Compare your answer: