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Note: You will find guidance on using inequalities to represent real-world problems here (towards the foot of the page).

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## Inequalities for word problems (page 1 of 2)

Name:______________________

Write an inequality to represent the situations described below and use them to help answer the questions.

Brett has a \$30 online gift voucher. He plans to buy as many books as he can. The cost of each book is \$4. There is also a single shipping charge of \$2. How many books can he afford without spending more than his gift voucher amount?

4n + 2 ≤ 30

He can afford a maximum of 7 books.

Sue and Cath have \$20 left for a cab fare home. The cab fare is \$3 per mile plus a \$2 fixed charge. What is the maximum number of miles they will be able to travel in the cab?

3n + 2 ≤ 20

The maximum distance they can travel is 6 miles.

Bert already has \$50 but needs a total of at least \$250 for his holiday. He gets paid £20 per day for delivering papers. What is the least number of days he must work to get enough money for his holiday?

20n + 50 ≥ 250

He must work at least 10 days.

Jennifer is planning a holiday. The hotel costs \$60 per night and her flights cost \$150. She has a budget of £500 for hotel and flights. Up to how many nights can she afford in the hotel?

60n + 150 ≤ 500

She can afford up to 5 nights in the hotel.

Commission or salary: Jill has a job offer. She is offered either \$50 per day or £30 per day plus a commission of \$3 for every plant she sells. How many plants does she need to sell to make the commission offer the best paying option?

30 + 3n > 50

She would have to sell at least 7 plants to make the commission offer the best paying option.

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## Inequalities for word problems (page 2 of 2)

Name:______________________

Write an inequality to represent the situations described below and use them to help answer the questions.

Lucas is offered either 15% or \$21 off his total shopping bill. How much would have to be spent to make the 15% option the best one?

0.15n > 21

Lucas would need to spend more than \$140 to make the 15% offer the best one.

Sid is \$300 in debt. He needs to get the debt down to no more than \$100 within the next 8 months. If he pays the same amount each month, what is the minimum he must pay off each month to manage this?

300 - 8n ≤ 100

He must pay a minimum of \$25 each month.

Joel is looking at costs for using a gym. He could pay \$50 per month for unlimited use or he could pay \$12 per month plus \$4 per visit. How many visits would he have to make each month to make the \$50 per month unlimited use option the cheapest one?

4n + 12 > 50

He would have to go to the gym at least 10 times each month to make the unlimited use option the cheapest.

Chantelle has signed up for hockey. Her parents set a limit of \$400 for costs for the season. It costs \$250 to sign up plus \$5 for each ice-time. What is the maximum number of ice-times that Chantelle can go to.

250 + 5n ≤ 400

The maximum number of ice times for Chantelle is 30.

Joe’s cell phone costs him \$21 per month plus \$3 for every 1GB of data downloaded. What is the limit to the number of GBs he can download to stay within his monthly budget of \$30.

21 + 3n ≤ 30

His limit is 3GB to stay within his budget.

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