Question

Joshua used 1/4 of a coil of rope to hold a shelf to the wall, kept 4/9 od the remainder and uses the rest equally to tie 2 parcels.

(a) What fraction of the rope did Joshua use to tie each parcel? Give your answer as a fraction in it's simplest form.

(b) Joshua had 240 cm of rope at first. How Ong was the rope he used to tie each parcel?

Answer 1

a)the fraction of rope that joshua used for each parcel is 16 2/3
b)the answer is 16.6 cm

Answer 2

Let the length of rope be 1 unit.Given Joshua used
`(1)/(4)` of a coil of rope to hold a shelf to the wall.

Remainder rope =
`1-(1)/(4) =(3)/(4)`

Joshua kept
`(4)/(9)` of the remainder

Rope kept by Joshua =
`(3)/(4) .(4)/(9) =(12)/(36) =(1)/(3)`

Rope left =
`(3)/(4) -(1)/(3) =(9-4)/(12) =(5)/(12)`

With this Joshua ties two parcels

a) Fraction of rope used to tie each parcel =
`(5)/(12)`÷2

=
`(5)/(12) .(1)/(2) =(5)/(24)`

b)Joshua has 240 cm of rope .

Rope used to tie each parcel =
`240.(5)/(24)` =50cm.