Words problems leading to inequalities are handled in a
similar fashion like the linear equations except that the equality sign (=) changes
to inequality sign.
Examples;
1. One-fifth
of a number added to two-third of the same number is greater than 26. Find the
range of values of the number.
Solution
Step
1
Let x represent the unknown number
The mathematical interpretation of the question will
be;
x/5 + 2x/3
> 26
Step
2
Multiply through by 15 which is the L.C.M of 5 and 3;
3x + 10x > 390
13x > 390
Step
3
Divide both sides by 13;
x > 390/13
x > 30.
Therefore, the range of values of x will be numbers
greater than 30, which are 31, 32, 33, 34, 35 …
2. Ade
bought x biros at #8 each and (x + 4) rulers at #20 each. He spent less than
#200. Form an inequality for the statement and solve it.
Solution
Step
1
Interpret the statement;
The biros cost #8x …….(1)
The rulers cost #20(x +4) …….(2)
Step
2
Expand the second statement and you will have;
(#20x + #80)
Step
3
Combining (1) and (2) gives the total cost of both
biros and rulers;
#(8x + 20x + 80) which is less than (<) #200.
Step
4
Forming an inequality equation below, you’ll have;
8x + 20x + 80 < 200
Step
5
Re-arrange and collect like terms;
Hence 28x < 200 – 80 (This is the inequality
statement)
28x < 120
Step
6
Divide both sides by 28;
x < 120/28
Therefore, x < 4.29.
Practice
these questions below;
1.
The sum of twice a number and 5 is less than the sum of one-third of the number
and 6.
2.
Two-thirds of a certain number is greater than the sum of the number and 6.
3. The
sum of twice a number and 15 is less than thrice the same number minus 9.
4. A
cyclist travels xkm in 4 hours, then (x + 60)km in 7 hours. Its average speed
does not exceed 150km/h.
5. A boy bought x mangoes at #5 and 3x oranges at #6. He collected some balance from #30.