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 can PLUG IN THE ANSWERS, which represent the length of the shorter piece.
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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