Posted by ckim on Friday, October 22, 2010 at 3:48am.
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.
someone please help me?!
- algebra - jai, Friday, October 22, 2010 at 5:13am
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,, :)
Answer This Question
More Related Questions
- Algebra - Here's another problem I'm having a little trouble with: A piece of ...
- Agebra - A 12ft. board is cut into two pieces so that one piece is 8 ft. longer ...
- algebra - a 38 inch piece of steels is cut into three pieces so that the second ...
- Math - A 12-ft. board is cut into 2 pieces so that one piece is 4 feet longer ...
- algebra - A 28-inch board is to be cut into three pieces so that the ...
- math - a 17 foot piece of string is cut into two pieces so that the longer piece...
- Math - A 14 inch board is to be cut into 3 pieces so that the second piece is ...
- algebra - A 40 inch board is cut into two pieces so that the shorter piece is ...
- Math - A 51 meter rope is cut into 2 pieces so that one piece is 6 meters longer...
- math - STRING LENGTHS: You have two pieces of string. One is 27 cm long. The ...