math

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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 -

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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