A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?
(A) 9
(B) 11
(C) 18
(D) 22
(E) 29
OA: B
Anyone please, explain the POE. Thanks.
OG2015 PS A rope 40 feet
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Hi lionsshare,lionsshare wrote:A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?
(A) 9
(B) 11
(C) 18
(D) 22
(E) 29
OA: B
Anyone please, explain the POE. Thanks.
This can certainly be solved through plug-in option values, but the algebraic approach is easier and a time-saver.
Say the length of the longer piece = x feet, the length of the shorter piece = x - 18.
=> Length of longer piece + Length of shorter piece = 40
Thus, x + (x - 18) = 40
2x = 58
So, x = 29
Thus the length of shorter piece = x - 18 = 29 - 18 = 11 feet.
The correct answer: B
Hope this helps!
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We can PLUG IN THE ANSWERS, which represent the length of the shorter piece.lionsshare wrote:A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?
(A) 9
(B) 11
(C) 18
(D) 22
(E) 29
Since the length of the shorter piece must be less than half of the total length of 40 feet, the shorter piece must be less than 20 feet long.
Eliminate D and E.
When the correct answer choice is plugged in, shorter + longer = 40.
B: shorter = 11 feet
Since the longer piece is 18 feet longer than the shorter piece, longer = 11+18 = 29.
shorter + longer = 11+29 = 40.
Success!
The correct answer is B.
Algebraic solution:
Let L = the longer piece and S = the shorter piece.
Since the total length is 40, we get:
L+S = 40.
Since the difference between the two lengths is 18, we get:
L-S = 18.
Adding together the two equations, we get:
(L+S) + (L-S) = 40+18
2L = 58
L = 29.
Since L is 18 feet longer than S, we get:
S = 29-18 = 11.
The correct answer is B.
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We can let L = the length of the longer piece of rope and S = the length of the shorter piece of rope.lionsshare wrote:A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?
(A) 9
(B) 11
(C) 18
(D) 22
(E) 29
We are given that the rope is 40 feet long. Translating this into an equation, we have:
L + S = 40
Next, we are given that one piece is 18 feet longer than the other. Translating this into an equation, we have:
L = 18 + S
We can now substitute 18 + S from the second equation for L in the first equation. We have:
18 + S + S = 40
2S = 22
S = 11
The shorter piece of rope is 11 feet.
Answer: B
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