INEQUALITY WORD PROBLEMS WORKSHEET

Problem 1 : 

Sum of a number and 5 is less than -12. Find the number.

Problem 2 : 

David has scored 110 points in the first level of a game. To play the third level, he needs more than 250 points. To play third level, how many points should he score in the second level ?

Problem 3 : 

An employer recruits experienced (x) and fresh workmen (y) for his firm under the condition that he cannot employ more then 9 people. If 5 freshmen are recruited, how many experienced men have to be recruited ? 

Problem 4 : 

On the average, experienced person does 5 units of work while a fresh one (y) does 3 units of work daily. But the employer has to maintain an output of at least 30 units of work per day. How can this situation be expressed ? 

Answers

Problem 1 : 

Sum of a number and 5 is less than -12. Find the number.

Answer :

Let x be the number.

Step 1 : 

Write the inequality.

x + 5 < -12

Step 2 :

Solve the inequality using Subtraction Property of Inequality.

Subtract 5 on from both sides. 

(x + 5) - 5 < -12 - 5

x < -17

So, the number is any value less than -17. 

Problem 2 : 

David has scored 110 points in the first level of a game. To play the third level, he needs more than 250 points. To play third level, how many points should he score in the second level ?

Answer :

Let x be points scored in the second level.

Step 1 : 

He has already had 110 points in the first level.  

Points scored scored in the second level  =  x

Total points in the first two levels  =  x + 110

Step 2 :

Write the inequality.

To play third level, the total points in the first two levels should be more than 250. So, we have

x + 110 > 250 

Subtract 110 on from both sides. 

(x + 110) - 110 > 250 - 110

x > 140

So, he has to score more than 140 points in the second level. 

Problem 3 : 

An employer recruits experienced (x) and fresh workmen (y) for his firm under the condition that he cannot employ more then 9 people. If 5 freshmen are recruited, how many experienced men have to be recruited ? 

Answer :

Step 1 : 

Write the inequality. 

x + y ≤ 9

Step 2 :

Substitute 5 for y.

x + 5 ≤ 9

Subtract 5 from both sides.

(x + 5) - 5 ≤ 9 - 5

x ≤ 4

To meet the given condition, no. of freshmen to be recruited can be less than or equal to 4. 

Problem 4 : 

On the average, experienced person does 5 units of work while a fresh one (y) does 3 units of work daily. But the employer has to maintain an output of at least 30 units of work per day. How can this situation be expressed ?

Answer :

Let x and y be the number of experienced person and fresh workmen respectively. 

Step 1 : 

From the given information, we have

Total number of units of work done by experienced person per day is 

=  5x

Total number of units of work done by fresh one per day is

=  3y 

Step 2 :

Total number of units of work done by both experienced person and fresh one per day is

=  5x + 3y 

As per the question, total number of units of work per day should be at least 30 units. 

That is, total number of units of work (5x+3y) should be equal to 30 or more than 30. 

So, we have 5x + 3y ≥ 30.

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