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In this lesson, we will learn how to formulate a multistep inequality in a real-world context and how to solve it to get the range of values satisfying that inequality.

Q1:

Sameh ran 600 meters in 90 seconds, while Amira was at least 9 seconds ahead of him. Write an inequality to represent the time Amira finished the 600-meter run.

Q2:

A moving company charges a flat rate of $150 and an additional $5 for each box. If a taxi service charged $20, for how many boxes would it be cheaper to move with the taxi service than with the moving company?

Q3:

In a board game, Maged scored 22, 11, 23, 19, and 17 points in five turns. Find the minimum number of points he must score in the sixth turn to have an average of at least 17 points.

Q4:

Fady wants to purchase a precision balance for $340. He has already saved $113 and can save $28 every week. Write an inequality that can be used to determine the number of weeks left for Fady to save at least $340.

Q5:

Amira finds two landscape gardeners online: the first charges a fixed fee of $20 per job plus $15 per hour for labor, while the second charges a fixed fee of $90 but only $5 per hour for labor. After how many hours will the second gardener be cheaper than the first?

Q6:

You are choosing between two different window-washing companies. The first charges $ 5 per window, while the second charges a base fee of $ 4 0 plus $ 3 per window. How many windows would you need to have for the second company to be preferable?

Q7:

Fady finds two plumbers online: the first charges $20 per hour of labor, while the second charges a fixed charge of $40 per job plus an hourly labor charge of $15. After how many hours will the second plumber be cheaper than the first?

Q8:

Shady earns $6.75 an hour waiting on tables. He is saving money to buy a new video game which costs $27. Write an inequality to find how many hours Shady must work to buy the game, and then solve it.

Q9:

Adel has a total of $200 and wants to buy some Blu-ray discs. Given that Blu-ray discs cost $18.75 each, and he must save at least $65, write an inequality that can be used to find how many Blu-ray discs he can buy, and then determine the maximum number of Blu-ray discs he can buy.

Q10:

Mona has saved $31 in her piggy bank and her sister Rania has saved $36. If Rania saves $6 a week and Mona saves $9 a week, after how many weeks will Mona have saved more than Rania?

Q11:

You are choosing between two different prepaid mobile phone plans. The first plan charges a rate of 26 cents per minute. The second plan charges a monthly fee of $19.95 plus 11 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?

Q12:

A cell phone company offers the following two plans:

How many texts would you need to send per month for plan B to save you money?

Q13:

A car rental company offers two plans for renting a car.

How many miles would you need to drive for plan B to save you money?

Q14:

Q15:

When hired at a new job selling jewelry, you are given two pay options:

How many dollars’ worth of jewelry would you need to sell for option A to produce a larger income?

Q16:

A basic cellular package costs $20 per month for 60 min of calling, with an additional charge of $0.30 per minute beyond that time. The cost formula would be 𝐶 = $ 2 0 + 0 . 3 0 ( 𝑥 − 6 0 ) , where 𝑥 is the number of minutes used. Given that your monthly bill must be less than $50, find the maximum number of minutes you can use in a month.

Q17:

Nabil and Adam are competing on a quiz app. Nabil has 400 points and is losing 2 points per minute; Adam has 250 points and is winning 10 points per minute.

Write an inequality which can be used to find , the amount of time for which Nabil has no fewer points than Adam.

Use your inequality to find the time when Adam catches up with Nabil. Assume that points are won or lost at a constant rate.

Q18:

The cost of producing “doomflots” is $325 for equipment plus another $32 for materials and labor for each one produced. How many “doomflots” need to be produced such that the average cost per “doomflot” is less than $50?

Q19:

Shady and Sally were saving their allowances. Shady has started with $150 in his account and deposited $20 at the end of every month; Sally started with $50 in her account and deposited $32 at the end of every month.

Write an inequality that can be used to find , the number of months for which there was more money in Shady’s account than in Sally’s.

Use your inequality to find .

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