Question

​120 inch length of ribbon is to be cut into three pieces. The longest piece is to be 40 inches longer than the shortest​ piece, and the third piece is to be half the length of the longest piece. Find the length of each piece of ribbon.

Answer 1

Let x = length of shortest piece. You want to express everything in terms of x, then add them in an equation you can solve for x.

Longest piece = 40 + x.

Medium piece = (40 + x)/2 OR 20 + 1/2x.

Shortest piece = x.

You know all the pieces combined = 120 inches, so add all the expressions:

40 + x + 20 + 1/2x + x = 120. Add the whole numbers first, then add the variables:

60 + 2.5x = 120. (note that I made 1/2x into 2.5x for the purpose of plugging in to a calculator in the next step).

Subtract 60 from the left side and the right side:

2.5x = 60

x = 60/2.5 = 24

So, finally...

shortest = 24 in
longest = 64
medium = 32

Want to check your work? Add shortest, longest, and medium, and you'll see it all adds up to 120 inches! :)

Answer 2

Also just thought I should clarify where I got the 2.5x from - x + x = 2x and 1/2x = .5x, so 2x + .5x = 2.5x.

I didn't want it to seem like I said that ONLY 1/2x simplifies to 2.5x - that's x + x + 1/2x!

Answer 3

shortest = x
longest = x+40
middle = (x+40)/2
so
x +(x+40) + (x+40)/2 = 120

x + x +40 +.5 x +20 = 120

2.5 x = 60

x = 24
(x+40)/2 = 32
(x+40) = 64