Question

A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?
a.22 feet
b.26 feet
c.33 feet
d.44 feet

Answer 1

So if one bit of the length, is half the size of the other bit then we can make the following equation, for x being the length of rope:

x + 2x = 66
3x = 66
x = 22

That is the length, of the smaller one (half the big one), so 2x = 44. Hence d) is your answer.

Hope I helped!

Answer 2

Let's say the two piece's lengths are x and y

so x+y=66

then we are told that "one piece is half the length of the other"
so x = (1/2)y

we plug this into the first equation and get
(1/2)y + y = 66
or
1.5 y = 66

divide both sides by 1.5 to get y alone
y = 66 / 1.5 = 44

we can check to see if y is the longer one by finding x
x = 66 - y = 66 - 44 = 22

44 is bigger than 22
therefore 44 is the length of the longer piece