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# A piece of twine of length t is cut into two pieces. The length of the

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A piece of twine of length t is cut into two pieces. The length of the  [#permalink]

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15 Jul 2018, 08:49
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A piece of twine of length t is cut into two pieces. The length of the longer piece is 2 yards greater than 3 times the length of the shorter piece which of the following of the length, in yards, of the longer piece

(A) $$\frac{(t+3)}{3}$$

(B) $$\frac{(3t+2)}{3}$$

(C) $$\frac{(t-2)}{4}$$

(D) $$\frac{(3t+4)}{4}$$

(E) $$\frac{(3t+2)}{4}$$

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A piece of twine of length t is cut into two pieces. The length of the  [#permalink]

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15 Jul 2018, 12:22
Total length of the twine = t

longer piece : l

shorter piece= t-l

Given , l=2+3(t-l)

by solving , t= (3t+2)/4

Ans E
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A piece of twine of length t is cut into two pieces. The length of the  [#permalink]

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15 Jul 2018, 12:57
Bunuel wrote:
A piece of twine of length t is cut into two pieces. The length of the longer piece is 2 yards greater than 3 times the length of the shorter piece which of the following of the length, in yards, of the longer piece

(A) $$\frac{(t+3)}{3}$$

(B) $$\frac{(3t+2)}{3}$$

(C) $$\frac{(t-2)}{4}$$

(D) $$\frac{(3t+4)}{4}$$

(E) $$\frac{(3t+2)}{4}$$

I Algebra

$$t=$$ length of twine
$$S=$$ length of shorter piece
$$L=3S + 2 =$$ length of longer piece
$$L - 2 = 3S$$
$$\frac{L-2}{3}=S$$

$$L+S=t$$
$$L + \frac{(L-2)}{3}=t$$
$$3L +(L-2)=3t$$
$$4L=3t+2$$
$$L=\frac{(3t+2)}{4}$$

II. Assign values
Let smaller length, S = 1 yard
Longer length, L = (3S + 2) = (3 + 2) = 5 yds
Twine length, t = (S + L) = (1 + 5) = 6 yds

Using t=6, find the answer that yields L = 5

(A) $$\frac{(t+3)}{3}=\frac{(5+3)}{3}=\frac{8}{3}$$ NO

(B) $$\frac{(3t+2)}{3}=\frac{(3*6)+2}{3}=\frac{20}{3}=6.xx$$ NO

(C) $$\frac{(t-2)}{4}=\frac{(6-2)}{4}=1$$ NO

(D) $$\frac{(3t+4)}{4}=\frac{(3*6)+4}{4}=\frac{22}{4}=5.5$$ NO

(E) $$\frac{(3t+2)}{4}=\frac{(3*6)+2}{4}=\frac{20}{4}=5$$ YES

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Re: A piece of twine of length t is cut into two pieces. The length of the  [#permalink]

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25 Jul 2018, 10:23
First algebraically, SP= shorter piece, LP=longer piece.
3(SP)=LP-2yards
LP+SP=t (the variable t is given by the author).
We need to show LP in terms of t variable.
If LP+SP=t, therefore SP=t-LP. So now we can plug this into our above equation.
3(t-LP)=LP-2yards --> 3t-3LP=LP-2 --> 3t=4LP-2 --> 4LP=3t+2 --> LP= 3t+2/4
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Re: A piece of twine of length t is cut into two pieces. The length of the &nbs [#permalink] 25 Jul 2018, 10:23
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