find the length of the longer string

Question

Jing Liang cut a rope into two pieces that have lengths in ratio of 3:8.If the difference between the lengths of the two pieces of strings is 95cm,find the length of the longer string

Answer 1

If the string is s cm long,

the shorter piece is (3/11)s cm

the longer piece is (8/11)s cm

 

The difference is 95cm:

(8/11)s - (3/11)s = 95

(5/11)s = 95

s = 95(11/5)

s = 209 cm for full length

 

The longer piece is (8/11)(209) = 152 cm

 

The shorter piece is 57 cm