Problema Solution
A length of string is cut in half and one half is used. The one third of the other half is cut off and used. If the remaining string is 10 metres long, how long was the original string?
Answer provided by our tutors
Let 'x' be the length of the original string.
(1/2)x of the string is used then x-(1/2)x = (1/2)x is left.
(1/3)(1/2)x is used and the remaining is (1/2)x - (1/3)(1/2)x = (2/3)(1/2)x
Also the remaining string is 10 m long so we have
(2/3)(1/2)x = 10
(2/6)x = 10
x = 10 * 6 / 2
x = 30 meters
Indeed:
30/2 = 15 was used, 15 was left
1/3 of 15 is 5 is used
15 - 5 = 10 is left
The original string was 30 meters long.