# Inequalities for word problems

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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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### Related Resources

The various resources listed below are aligned to the same standard, (7EE04) taken from the CCSM (Common Core Standards For Mathematics) as the Expressions and equations Worksheet shown above.

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

• Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
• Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid \$50 per week plus \$3 per sale. This week you want your pay to be at least \$100. Write an inequality for the number of sales you need to make, and describe the solutions.

#### Worksheet

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Solve real-life and mathematical problems using numerical and algebraic expressions and equations

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