# algebra

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a piece of wire that is 58cm long is cut into three pieces. the longest piece is 6cm shorter than the sum of the lengths of the other two pieces. five times the lengths of the shortest piece is 10cm less than the sum of the lengths of the other two pieces. determine the lengths of the three pieces of wire.

• algebra -

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,, :)