Question

a rope 250cm long is cut into four parts such that the firzt part is twice as long as the second, the second is 10 cm longer than the third and third is 5cm shorter than fourth. find the length of each part

Answer 1

total length of rope = 250cm
=> the sum of four parts is the total length.
it is cut into 4 parts.

fourth part = x.

third part is 5cm less than fourth
so third part = x-5

second part is 10cm longer than third
so second part = (x-5)+10 = 10+x-5 = 5+x

first part is twice as long as second
so first part = 2(10+x-5) = 20+2x-10 = 10+2x

:. total length of rope = sum of 4 parts.
250 = x + (x-5) + (5+x) + (10+2x)
= x+x-5+5+x+10+2x
250 = 5x+10
250-10 = 5x
240/5 = x
:. x = 48

therefore,
fourth part = x = 48cm
third part = x-5 = 48-5 = 43cm
second part = 5+x = 5+48 = 53cm
first part = 10+2x = 10+2×48 =106cm