Linear Inequations-25

From Homeworkwiki

Jump to: navigation, search

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 third length is to be
twice as long as the shortest. What are the possible lengths for the shortest board
if third piece is to be at least 5 cm longer than the second?

Solution: Let the length of the shortest piece be x cm.

Then, the lengths of the second and third piece are x + 3 cm and 2x cm respectively. Then,

x + (x + 3) + 2x ≤ 91 and 2x ≤ (x+ 3) + 5

=> 4x + 3 ≤ 91 and 2x ≥ x + 8

=> 4x ≤ 88 and x ≥ 8

=> x ≤ 22 and x ≥ 8

=> 8 ≤ x ≤ 22

Hence, the shortest piece must be at least 8 cm long but not more than 22 cm long.

Personal tools
McAfee SECURE sites help keep you safe from identity theft, credit card fraud, spyware, spam, viruses and online scams