Terrence has a length of rope that is #14 3/14# meters long. Forty percent of the rope's length is covered by a plastic film that makes it waterproof. What length of the rope is not waterproof?

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Answer 1 · 2017-10-17T17:23:43

See a solution process below:

First, to make things easier, let's convert the length of the rope from a mixed number to an improper fraction:

#14 3/14 = 14 + 3/14 = (14/14 xx 14) + 3/14 = 196/14 + 3/14 = 199/14#

If 40% of the rope is covered in plastic film then 60% of the rope is not. (100% - 40% = 60%)

To find the the length of rope that is not waterproof we need to find:

What is 60% of #199/14#

"Percent" or "%" means "out of 100" or "per 100", Therefore 60% can be written as #60/100#.

So we can write and evaluate:

#60/100 xx 199/14 =>#

#(60 xx 199)/(100 xx 14) =>#

#11940/1400 =>#

#(20 xx 597)/(20 xx 70) =>#

#(color(red)(cancel(color(black)(20))) xx 597)/(color(red)(cancel(color(black)(20))) xx 70) =>#

#597/70 =>#

#(560 + 37)/70 =>#

#560/70 + 37/70 =>#

#8 + 37/70 =>#

#8 37/70#

#8 37/70# meters of the rope is not waterproof.