# Linear Inequations-25

### From Homeworkwiki

**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.