A 6-ft. board is cut into 2 pieces so that one piece is 2 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
A shorter piece: 3 ft; longer piece: 18 ft
B shorter piece: 6 ft; longer piece: 20 ft
C shorter piece: 16 ft; longer piece: 18 ft
D shorter piece: 1 ft; longer piece: 5 ft
2007-12-07 05:49:19 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let A and B be the lengths of the pieces.
A + B = 6
A -2 = 3 B
Substitute A = 3 B + 2 into the first equation
3 B + 2 + B = 6
4 B = 4
B = 1
So the pieces are lengths 1 and 5 feet.
2007-12-07 05:52:33 · answer #1 · answered by jgoulden 7 · 1⤊ 0⤋
You really don't even have to know the algebra behind this. Look at your choices. Remember you are starting witha 6 ft board. so there is no way that you can break up a 6ft long board into two pieces with one of those pieces being 18ft, or 20ft, or 16ft. So you can rule out A,B, and C. but here is the algebra behind it.
x + (2 + 3x) = 6
4x + 2 = 6
4x = 4
x = 1
Is the shorter piece.
Now the longer piece is 2 more than 3 times x
2+3x
= 2+3(1)
= 5
is the longer piece
D
2007-12-07 05:52:57 · answer #2 · answered by Jeƒƒ Lebowski 6 · 0⤊ 0⤋
Sometimes it helps to read all the answers before you start trying to figure out what math to use.
How long is the original board? 6 feet. OK, then, how can any of the cut sections of the board be longer than 6 feet?
Without doing any math, you know the answer is D. If you check it, 3 x 1 is 3 plus 2 is 5.
2007-12-07 05:59:06 · answer #3 · answered by historian 4 · 0⤊ 0⤋
3x+2+x=6
4x=4
x=1 choice D
2007-12-07 05:53:43 · answer #4 · answered by chasrmck 6 · 1⤊ 0⤋
6= x + y
3x + 2 = y
6 = 4x + 2
4x = 4
x = 1
alternative D
That is it!!! OK !!!
2007-12-07 05:55:53 · answer #5 · answered by tiago_provenzano 3 · 0⤊ 0⤋
d
2007-12-07 05:53:40 · answer #6 · answered by daniel 4 · 1⤊ 0⤋
b
2007-12-07 05:52:34 · answer #7 · answered by lovelymomma 1 · 0⤊ 2⤋