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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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Show Answers

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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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.*

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*

- Equations with subtraction e.g. x - 4 = 2 (From Worksheet)
- Equations with division e.g. n/2 = 12 (From Worksheet)
- Subtraction & addition equations (1 of 2) e.g. a + 3 = 7 and x - 9 = 11 (From Worksheet)
- Subtraction & addition equations (2 of 2) e.g. a + 3 = 7 and x - 9 = 11 (From Worksheet)
- Multiplication & division equations (1 of 2) e.g. 3n = 12 and a/7 = 3 (From Worksheet)
- Multiplication & division equations (2 of 2) e.g. 3n = 12 and a/7 = 3 (From Worksheet)
- Addition, subtraction, multiplication & division equations (From Worksheet)
- Addition, subtraction, multiplication & division equations (From Worksheet)
- Solving equations in two steps (1 of 4) e.g. 5n + 4 = 29 (From Worksheet)
- Solving equations in two steps (2 of 4) e.g. a/4 + 3 = 7 (From Worksheet)
- Solving equations in two steps (3 of 4) e.g. 7n - 3 = 18 (From Worksheet)
- Solving equations in two steps (4 of 4) e.g. b/9 - 4 = 6 (From Worksheet)