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Woody19
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A piece of cloth costs $35. If the length of the piece Updated on: 13 Jul 2019, 10:50
Originally posted by Woody19 on 10 Jul 2019, 22:56.
Last edited by Woody19 on 13 Jul 2019, 10:50, edited 1 time in total.
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55% (hard)

Question Stats:

70% (02:51) correct 30% (02:30) wrong based on 63 sessions

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Q. A piece of cloth costs $35. If the length of the piece had been 4 meters longer and each meter costs $1 less , the cost would have remained unchanged.
How long is the piece?

A. 9 m

B. 10 m

C. 11 m

D. 12 m

E. 13 m

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A piece of cloth costs $35. If the length of the piece 11 Jul 2019, 00:16
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A piece of cloth costs $35. If the length of the piece had been 4 meters long and each meter costs $1 less , the cost would have remained unchanged.
How long is the piece?

Let length of cloth be =L
Cost of unit length of cloth be=C

L*C= (L+4)*(C-1)=35

Check Options:

(A) If L =9 ---> C=35/9 But, with these values, \((L+4)*(C-1)\neq{35}\) -->Eliminate

(B) If L=10 ----> C=35/10=3.5; (L+4)*(C-1)=(14)*(2.5)=35, satisfies the condition. Correct Ans
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A piece of cloth costs $35. If the length of the piece 13 Jul 2019, 09:54
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Shouldn't the correct wording be that the cloth is '4 meters longer' instead of '4 meters long' ?
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A piece of cloth costs $35. If the length of the piece 13 Jul 2019, 10:51
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tortiees That was a typo. Edited Thank you.
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A piece of cloth costs $35. If the length of the piece 13 Jul 2019, 13:45
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Quote:
Q. A piece of cloth costs $35. If the length of the piece had been 4 meters longer and each meter costs $1 less , the cost would have remained unchanged.
How long is the piece?

Let us say that our previous length was x. Then a new length is x + 4
Also, let us represent our cost not with a second variable, instead let us represent it via price and length. In this case previous cost was 35 / x. The new cost, respectively, is 35 / x - 1.
Let us show it now with expression. As the total cost remained unchanged, then (x + 4) * (35 / x - 1) = 35
(x + 4) * ((35 - x) / x) = 35 ==> (35 - x) / x = 35 / (x + 4) ==> (35 - x) * (x + 4) = 35x ==> 35x + 140 - x ^ 2 - 4x = 35x ==> x^2 + 4x - 140 = 0

Via discriminant we get that x1 = 10 and x2 = - 14. The length cannot be negative, thus the answer is 10.

Answer: B

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