Problem 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.
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 ?
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.
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 ?
Solution :
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 ?
Solution :
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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