Posted by ckim on Friday, October 22, 2010 at 3:48am.
represent the unknowns using variables:
let x = shortest piece
let y = 2nd longest piece
let (x+y) - 6 = longest piece *according to the 2nd statement*
set up equations:
(1) x + y + (x+y) - 6 = 58
*total length must be 58*
(2) 5x = y + (x+y) - 6 - 10
*according to 3rd statement*
these equations are simplified to:
(1) y = 32 - x
(2) y = 2x + 8
we then substitute the first equation to the second, o that everything will be in terms of x,, or you can do the other way around:
32 - x = 2x + 8
-3x = -24
x = 8 cm [length of shortest]
*using the simplifies equation (1), we get y:
y = 32-x = 24 cm [length of 2nd longest]
(x+y)-6 = 26 cm [length of longest]
**to check, see if their sum is equal to 58 cm,,
so there,, :)
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