Emily K.

asked • 04/15/15

52 foot long chain

A 52 foot long chain is divided into 3 parts. The second piece is 2 feet longer than the first. The third piece is 1 foot shorter than the first.
 
A) How long is each piece of the chain?
 
B) show how to check your answer

Kaylie H.

This is the chain, split into three separate parts. 
 
_______ | ________ | _______      (not to scale)
 
                   =52
Since the second and third parts are based off of the first one, we need to use a variable as a basis. Let's use (x), represented in feet.
 
_______ | ________ | _______
    x
 
We know the second part is 2 feet longer than the first, so we can label that as x+2 (first part, plus two feet, equals second part)
 
_______ | ________ | _______
     x             x+2
 
We know the third part is 1 foot shorter than the first, so we can label that as x-1 (first part, minus one foot, equals third part)
 
_______ | ________ | _______
     x             x+2           x-1
 
We know these three parts added together will give you 52. so we set up the equation:
 
(x)+(x+2)+(x-1)=52      without parenthesis: x+x+2+x-1=52
3x+1=52           Simplify the left side
3x=51               Subtract the 1 from both sides
x=17                 Divide by 3 on both sides
 
Knowing that x=17, we can conclude:
1st part (x) = 17
2nd part (x+2) =19
3rd part (x-1) =16
 
To check:
_______ | ________ | _______
    17     +      19      +     16 
                 =52 feet
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04/15/15

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