Posted by **professor kitty** on Tuesday, September 22, 2009 at 12:08am.

a piece of string is cut in half, so that one half can be used to tie newspapers, one third of the remaining string is cut off to tie a parcel. the leftover string is 2m long. how long was the whole string

- math -
**DrBob222**, Tuesday, September 22, 2009 at 12:40am
String is x meters long.

The string is cut in 1/2 so now we have 2 halves, each half is (1/2)*x or x/2.

We take 1/3 of the x/2 piece to tie a parcel. How much is left? That will be

(1/2)(x)-(1/3)(x/2) and that piece is 2 m.

So (1/2)(x)-(1/3)(x/2) = 2 m

or (1/2)(x)-(1/6)(x) = 6

Solve for x.

Multiply through by 6.

3x-x=12

2x = 12

x = 6,

Check:

String is 6 meters long.

We cut half of it leaving 3 meters.

3 meters used to tie newspaper.

The 3 meter piece that's left is cut to remove 1/3 of that. 1/3*3 = 1 meter used to tie a parcel. That leaves 2 meters for the part left over and that's what the problem says.

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