Carcass wrote:
A board of length L feet is cut into two pieces such that the length of one piece is 1 foot more than twice the length of the other piece. Which of the following is the length, in feet, of the longer piece?
(A) \(\frac{L + 2}{2}\)
(B) \(\frac{2L +1}{2}\)
(C) \(\frac{L-1}{3}\)
(D) \(\frac{2L+ 3}{3}\)
(E) \(\frac{2L+1}{3}\)
Plugging in numbers can lead us astray here.
Let's assume that the longer and shorter sides are A and B, respectively.
Let
B = 1.
Let
A = 2B + 1 = 2(1) + 1 = 2 + 1 = 3.
So, the
total length is 3 + 1 = 4.
The correct choice should evaluate to produce the length of A.
(A) (4+2)/2 = 6/2 =
3 This equals the length of A.
(B) ((2*4) + 1)/2 = (8+1)/2 = 9/2 = 4.5
(C) (4 - 1)/3 = 3/3 = 1
(D) (2*4+3)/3 = (8+3)/3 = 11/3
(E) (2*4+1)/3 = (8+1)/3 = 9/3 =
3 This equals the length of A.
Both A and E equal 3, the length of the longer side, when we evaluate by picking numbers.That being said, E is the original answer, so we have to find a way to get to that and only that reliably.
For that reason, I think the algebraic solution offered by
HarishKumar was very good.
Cheers!