SOLUTION: A board 25 feet long is cut into two pieces. Five feet less than two times the length of the longer piece is equal to three times the length of the shorter piece. Find the length o

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Question 1112450: A board 25 feet long is cut into two pieces. Five feet less than two times the length of the longer piece is equal to three times the length of the shorter piece. Find the length of each piece.
Found 2 solutions by ankor@dixie-net.com, Theo:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A board 25 feet long is cut into two pieces.
L + s = 25
s = -L + 25
Five feet less than two times the length of the longer piece is equal to three times the length of the shorter piece.
2L-5 = 3s
replace s with (-L+25)
2L - 5 = 3(-L+ 25)
2l = -3L + 75 + 5
2L + 3L = 80
5L = 80
L = 80/5
L = 16
find s
s = -16 + 25
s = 9
Find the length of each piece.
Longer = 16, shorter = 9
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Check
"Five feet less than two times the length of the longer piece is equal to three times the length of the shorter piece.
2(16) - 5 = 3(9)
32 - 5 = 27

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let x = the length of the longer piece.
let y = the length of the shorter piece.

the board is 25 feet long.

the length of the longer piece plus the length of the shorter piece is equal to 25 feet.

the equation for that is x + y = 25 (first equation)

Five feet less than two times the length of the longer piece is equal to three times the length of the shorter piece.

the equation for that is 2x - 5 = 3y (second equation)

these two equations need to be solved simultaneously.

in the first equation, solve for y to get y = 25 - x.

in the second equation, replace y with 25 - x to get:

2x - 5 = 3y becomes 2x - 5 = 3 * (25 - x)

simplify to get:

2x - 5 = 75 - 3x

add 3x to both sides of the equation and add 5 to both sides of the equation to get:

5x = 80

solve for x to get x = 80/5 = 16

in the first equation, replace x with 16 to get x + y = 25 becomes 16 + y = 25

solve for y to get y = 25 - 16 = 9.

you have x = 16 and y = 9.

the first equation of x + y = 25 becomes 16 + 9 = 25 which becomes 25 = 25 which is true.

the second equation of 2x - 5 = 3y becomes 2 * 16 - 5 = 3 * 9, which becojmes 32 - 5 = 27, which becomes 27 = 27, which is true.

both original equations are true when x = 16 and y = 9, therefore the solution can be assumed to be good.

your solution is that the length of the longer piece is 16 feet and the length of the shorter piece is 9 feet.