In this section, you will learn how to create an inequality for the given word problem by using algebraic reasoning and solve for the unknown quantity.
Example 1 :
Sum of a number and 5 is less than -12. Find the number.
Solution :
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.
Example 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 ?
Solution :
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.
Example 3 :
An employer recruits experienced and fresh workmen 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 ?
Solution :
Let x be the no. of freshmen to be recruited.
Step 1 :
Write the inequality.
x + 5 ≤ 9
Step 2 :
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.
Example 4 :
An employee of a factory has to maintain an output of at least 30 units of work per week. If there are five working day in a week, how many units of work to be done by him per day ?
Solution :
Let x be the no. of units of work done per day.
Step 1 :
From the given information, we have
Total number of units of work done per week = 5x
Step 2 :
Write the inequality.
As per the question, total number of units of work done per week should be at least 30 units. So, we have
5x ≥ 30
Divide both sides by 5
5x/5 ≥ 30/5
x ≥ 6
So, the number of units of work to be done per day should be at least 6.
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