Free Study Material

NCERT Solutions

NCERT Books

Revision Notes

Practice Problems

This is one of our many quizzes on Graphing inequalities. Click on this to access more such competitive quizzes on Algebra.

Graphing inequalities Quiz 2

mathematics

 Ross won 42 candies at the local fair. He gave one away to every student in his class. He now has at least 7 candies left. If the number of students in his class is ‘n’ Find the relation. 

 Here the relation that exists is Leftover candies $=$ Total candies $-$ candies not distributed. Substitute the values to find the relation and answer.

  Given candy per student $=1$ and Candies left $\ge \text{7}$ $ \\ $ Leftover candies $=$ Total candies $-$ candies not distributed $ \\ $ Leftover candies $=42 - 1n \ge \text{7}$ $ \\ $ So the relation is $\text{42 - n}\ge \text{7}$ $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/00a7c89a-0ed5-493a-a9a3-319f4f30b7062879809817116248058.png"/>

 Barney bought a magazine and 4 books for less than Rs 26. If the magazine cost Rs. 6.Let the cost of the book be $z$. What is the price of the book, if it is an integral value?

  Cost of magazine $=6$ and Cost of book$=z$  $ \\ $ Amount spent $=$ Cost of book $+$ $4($cost of magazine$)$  $ \\ $ Amount spent $=4z+6 < 26$ $ \\  4z < 26 - 6 \\  \Rightarrow {4z < 20} \\ \Rightarrow z < 5 \\ $ $z$ is not equal to $5$, so the least time possible price is $4$. $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/aa1b385c-9ba8-4430-830a-a1f99ab4713849644628156432658.png"/>

 I walk my dog more than 28 minutes everyday. If ‘T’ is the time represented in minutes that I walk my dog for, what would the relation be?

 Here the relation that exists is “Time $I$ walk the dogtime given”. Substitute the values to find the relation and answer.

Time $I$ walk the dog $> 28$ mins $ \\ $ Time $I$ walk the dog is represented as $T$ $ \\ $ So the relation is $ \\ \Rightarrow T > 28 \\ $  The graph of this inequality is $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/914989cf-a02b-4b2c-b21e-165bf01681fa3127010623821479352.png"/>

 More than 340 refugees were extracted, such that 11 buses were filled and 10 refugees travelled in cars.  How many refugees were present in each bus? 

 Here the relation that exists is “Total Refugees $= ($Refugees per bus$) \times ($number of buses$) + ($Refugees in Car$)$”. Substitute the values to find the relation and answer.

 Given number of buses $=10$ and Refugees in car $=10$  $ \\ $ Total Refugees $= ($Refugees per bus$)\times ($number of buses$) + ($Refugees in Car$)$  $ \\ $ Let Number of refugees per bus be $s$ $ \\ $ Total Refugees $=11s + 10 \ge 340$ $ \\  \text{11s}\ge 340-10 \\  \Rightarrow 11\text{p }\ge 330 \\  \Rightarrow p\text{ }\ge 30 \\ $ The graph of this equation will be as $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/d5801d7c-46a1-42e3-8197-db27085ab5ef8518632701753076537.png"/>

 A musician sold no more than 305 million records. 25 million records were sold by CDS and the rest were sold as a packaged deal with 7 record label houses. Let the number of records sold to each record label house be $x$. What is the relation between the unknowns? $($Scale the million to single part to simplify$)$

 Here the relation that exists is Total records sold $= ($records per record label house$) \times ($number of  record label houses$) + ($base records sold$)$. Substitute the values to find the relation and answer.

 Scaling the records from 1 million to 1unit as $ \\ \text{1million=1unit} \\ $ Given number of record label houses $=7$ and Base Records sold $=25$  $ \\ $ Total records sold $= ($records per record label house$) \times ($number of  record label house$) + ($base records sold$)$ $ \\ $ Total records sold $=7x+25\le 305$ $ \\ \Rightarrow \text{7x+25}\le 305 \\ $ The graph of this equation will be as $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/f12860e4-88a3-4829-863c-f983a77e83332346282339471054004.png"/>