Inequality Word Problems 2

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Algebra 1

Inequalities

Inequality Word Problems

Inequality Word Problems 2

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Question 1 of 5

Michael wants to buy a new 4K HD TV. The cheapest TV is advertised as

$ 1100

$$1100$ . He has saved

$ 300

$$300$ already and has a part-time job earning

$ 160

$$160$ per week. How many weeks will it take before he has saved up enough to buy the cheapest TV?

1. $n$ $n$ $>$ $>$ $5$ $5$
2. $n \leq 5$ $n≤5$
3. $n$ $n$ $<$ $<$ $5$ $5$
4. $n \geq 5$ $n≥5$

Question 2 of 5

2. Question
A hard drive holds about $75$ $75$ hours of movie videos. So far it has $52$ $52$ hours. You estimate that each movie is $2$ $2$ hours long. How many movies can we transfer on top of the movies that are already in the hard drive?
- 1. $n \leq 11$ $n≤11$
- 2. $n \geq 11$ $n≥11$
- 3. $n$ $n$ $>$ $>$ $11$ $11$
- 4. $n$ $n$ $<$ $<$ $11$ $11$
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Identify the known values

$Size of hard drive = 75$ $\text(Size of hard drive)= 75$

$Hours already on hard drive = 52$ $\text(Hours already on hard drive)= 52$

$Number of hours per movie = 2$ $\text(Number of hours per movie)= 2$

$Number of movies = n$ $\text(Number of movies)= n$

First, form an inequality from the problem

Since the hard drive only has a capacity of $75$ $75$ hours, the total number of $2$ hour movies to be added on top of the $52$ hours worth that is already on the hard drive must be less than or equal to $75$ .

Hence, the inequality can be written as:

$52+2n$ $≤$ $75$

Next, make sure that only $n$ is on the left side

$52+2n$ $≤$ $75$

$52+2n$ $-52$ $≤$ $75$ $-52$ Subtract $52$ from both sides

$2n$ $divide2$ $≤$ $23$ $divide2$ Divide both sides by $2$

$n$ $≤$ $11.5$

Since we can only add a whole movie and we cannot go over $75$ , we need to round down the answer to $n≤11$

$n≤11$

Question 3 of 5

James currently weighs

$108$ kg. He wants to weigh less than

$90$ kg. If he can lose an average of

$1 1/2$ kg per week through exercise and diet, how long will it take to reach his goal?

1. $n$ $<$ $12$
2. $n≤12$
3. $n$ $>$ $12$
4. $n≥12$

Question 4 of 5

A medium-sized bag of potatoes weighs

$1$ kg more than a small bag. A large bag weighs

$4$ kg more than a small bag. If the total weight is at most

$14$ kg, what is the most that a small bag could weigh?

1. $s≤3$
2. $s≥3$
3. $s$ $<$ $3$
4. $s$ $>$ $3$

Question 5 of 5

5. Question
Jack is flying an air balloon at an altitude of $16000$ feet and is experiencing some bad weather. For him to fly safely, Jack needs to increase his altitude to at least $17000$ feet or decrease his altitude to no more than $13000$ feet. Form an inequality.

The number lines below are scaled as $1:1000$ ft
- 1.
- 2.
- 3.
- 4.
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A compound inequality consists of two inequalities joined together by AND or OR.

First, form an inequality from the problem

The height of the balloon must be at least $17000$ feet

$h$ $≥$ $17000$

The height of the balloon must be no more than $13000$ feet

$h$ $≤$ $13000$

$h≥17000$ OR $h≤13000$

The first given inequality has a greater than or equal to ( $≥$ ) sign.

Hence, place a solid circle above $17000$ and attach an arrow pointing to the right to represent all values greater than $17000$ .

The second given inequality has a less than or equal to ( $≤$ ) sign.

Hence, place a solid circle above $13000$ and attach an arrow pointing to the left to represent all values less than $13000$ .

Finally, combine the two number lines.

$300 + 160 n$ $300+160n$	$\geq$ $≥$	$1100$ $1100$
$300 + 160 n$ $300+160n$ $- 300$ $-300$	$\geq$ $≥$	$1100$ $1100$ $- 300$ $-300$	Subtract $300$ $300$ from both sides
$160 n$ $160n$ $\div 160$ $divide160$	$\geq$ $≥$	$800$ $800$ $\div 160$ $divide160$	Divide both sides by $160$ $160$
$n$ $n$	$\geq$ $≥$	$5$ $5$

$108-1 1/2n$	$<$	$90$

$108-1 1/2n$ $-108$	$<$	$90$ $-108$	Subtract $108$ from both sides

$-1 1/2n$ $divide(-1 1/2)$	$<$	$-18$ $divide(-1 1/2)$	Divide both sides by $-1 1/2$

$n$	$>$	$12$	Flip the inequality

Inequality Word Problems 2

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Quiz summary

Information

1. Question

Hint

Keep Going!

Identify the known values

2. Question

Hint

Fantastic!

Identify the known values

3. Question

Hint

Well Done!

Identify the known values

4. Question

Hint

Correct!

Identify the known values

5. Question

Hint

Exceptional!

Quizzes

$52+2n$	$≤$	$75$
$52+2n$ $-52$	$≤$	$75$ $-52$	Subtract $52$ from both sides
$2n$ $divide2$	$≤$	$23$ $divide2$	Divide both sides by $2$
$n$	$≤$	$11.5$

$S$ $+$ $M$ $+$ $L$	$≤$	$14$
$s$ $+$ $s+1$ $+$ $s+4$	$≤$	$14$	Substitute the known values
$3s+5$	$≤$	$14$	Combine like terms
$3s+5$ $-5$	$≤$	$14$ $-5$	Subtract $5$ from both sides
$3s$ $divide3$	$≤$	$9$ $divide3$	Divide both sides by $3$
$s$	$≤$	$3$

The height of the balloon	must be at least	$17000$ feet
$h$	$≥$	$17000$
The height of the balloon	must be no more than	$13000$ feet
$h$	$≤$	$13000$