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