Question

Question 26 A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?

[Hint: If x is the length of the shortest board, then x, (x + 3) and 2x are the lengths of the second and third piece, respectively. Thus, x = (x + 3) + 2x ≤ 91 and 2x ≥ (x + 3) + 5]

Class X1 - Maths -Linear Inequalities Page 123

Answer 1

Let x cm is length of shortest board.
then, second length is (x + 3) cm
third side length = 2x cm
also given,
total length ≤ 91 cm
x cm + (x + 3) cm + 2x cm ≤ 91 cm
=> 4x + 3 ≤ 91
=> 4x ≤ 91 -3
=> 4x ≤ 88
=> x ≤ 88/4 = 22
x ≤ 22 cm ------------(1)

again,
third side ≥ second side + 5
2x ≥ (x + 3) + 5
x ≥ 8 cm ----------(2)

from eqns (1) and (2) length of shortest board should be greater then equal to 8 cm and less then equal to 22cm .
e.g x€[8, 22]