March 2017
Problem of the Month

The String Problem
from the International Singapore Maths Competition

Mary cut off 2/5 of a piece of string.   Later, she cut off another 14 m.   The ratio of the length of string remaining to the total length cut off is 1 : 3.

What is the length of the remaining string?

Solution to the Problem:

The answer is 10m.

Let L be the original length of the string, and R be what is remaining once you have cut the string twice.
We know that R = (L x 3/5) - 14m, and that ((L x 2/5) +14) /R = 3, or 2L/5 + 14 = 3R.
By substituting the first equation in the second we have 2L/5 + 14 = 9L/5 -42.
which rearranges to: 7L/5 = 56, or L = 40.
So R = 10m.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Jim Hooker	Johnson City, Tennessee
3. Kimberly Howe	Tuscaloosa, Alabama
4. Eliza Sheffield & Anna Vice	Tuscaloosa, Alabama
5. SreeRoopa Sankararaman	Singapore, Singapore
6. Brijesh Dave	Mumbai city, Maharashtra, India

Send any comments or questions to: David Pleacher