Question 262736
let a, b, c, d = the lengths of the 4 pieces, (d is the shortest)
:
Write an equation for each statement:
:
"A 257 foot rope is cut into 4 pieces."
a + b + c + d = 257
:
"The second piece is 3 feet longer than twice the shortest piece."
b = 2d + 3
:
"The third piece is three times the length of the shortest piece."
c = 3d
:
The last piece is 20 feet longer than half the shortest piece.(a is the only one left)
a = .5d + 20
:
 How long is the longest piece?
a + b + c + d = 257
:
replace a, b, c using the above equations
(.5d+20) + (2d+3) + 3d + d = 257
:
Combine like terms:
.5d + 2d + 3d + d + 20 + 3 = 257
:
6.5d + 23 = 257
:
6.5d = 257 - 23
:
6.5d = 234
d = {{{234/6.5}}}
d = 36 ft is the shortest piece
then
a = .5(36) + 20
a = 18 + 20
a = 38 
and
b = 2(36) + 3
b = 72 + 3
b = 75
and
c = 3(36) 
c = 108, this would be the longest piece
:
:
Check solution
38 + 75 + 108 + 36 =  257