Kate cut a 100-foot rope into two pieces. One piece was 5 feet longer than 4 times the length of the others. What is the length of each piece?

2 Answers
Jul 22, 2018

#color(blue)("Longer piece"=81" ft")#
#color(blue)("Shorter piece"=19" ft")#

Explanation:

Let the shorter piece of rope be

#x#.

Then the longer piece is 4 times this plus 5.

#4x+5#

The total length is 100 ft

#:.#

#4x+5+x=100#

Solve for #x#:

#5x=100-5=95#

#x=95/5=19#

Longer piece is:

#4x+5#

#4(19)+5=81#

Shorter piece is:

#x=19#

#81# feet & #19# feet

Explanation:

Let the #x# & #y# feet be the lengths of longer & shorter parts of rope of original length #100# feet.

The sum of lengths of cut-parts must be equal to the length of original rope hence

#x+y=100\ ............(1)#

Given that longer part of length #x# is #5# feet longer than #4# times the length of smaller part of length #y# hence

#x=4y+5#

#x-4y=5\ ..........(2)#

subtracting (2) from (1), we get

#x+y-(x-4y)=100-5#

#5y=95#

#y=95/5#

#y=19#

Setting above value of #y# in (1) as follows

#x+19=100#

#x=100-19#

#x=81#

Hence, the two parts of rope are #81# feet & #19# feet