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# The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD

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The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD  [#permalink]

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09 Jul 2018, 16:39
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The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD is equal to the cost of 4 pencils and the cost of book is equal to the cost of 6 pens. What is the ratio of the cost of a book to the cost of a CD ?

A) 9 : 4
B) 4 : 9
C) 2 :3
D) 3 : 2
E) 2 : 1
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The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD  [#permalink]

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09 Jul 2018, 17:44
selim wrote:
The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD is equal to the cost of 4 pencils and the cost of book is equal to the cost of 6 pens. What is the ratio of the cost of a book to the cost of a CD ?

A) 9 : 4
B) 4 : 9
C) 2 :3
D) 3 : 2
E) 2 : 1

The purposely NOT fancy way.

Everything is defined in terms of pens and pencils. Take the ratio of pens and pencils and define one in terms of the other.

(1) 4 pens cost the same as 6 pencils
4 PN = 6 PC
6 PC = 4 PN
PC = $$\frac{4}{6}=\frac{2}{3}$$PN

(2) One CD costs the same as 4 pencils
1CD = 4PC
CD cost in PNs?
From above, PC = $$\frac{2}{3}$$ PN
So 1CD = (4 *$$\frac{2}{3}$$PN)
1 CD = $$\frac{8}{3}$$ PN

(3) One book cost the same as 6 pens
1B = 6PN

(4) Book and CD cost in terms of PENS
1B = 6PN
1CD = $$\frac{8}{3}$$PN

(5) Ratio of book cost to CD cost?
$$\frac{B}{CD}=\frac{6}{(\frac{8}{3})}=(6*\frac{3}{8})=\frac{18}{8}=\frac{9}{4}$$

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Re: The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD  [#permalink]

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09 Jul 2018, 17:57
We can solve it by making the unit of comparison the same.

4 pens=6 pencils so 1 pen=1.5 pencils.

Cost of CD=4 pencils
Cost of Book=6 pens or 9 pencils.

Cost of Book to Cost of CD ratio=9:4. Ans is A.

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Re: The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD  [#permalink]

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09 Jul 2018, 17:59
selim wrote:
The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD is equal to the cost of 4 pencils and the cost of book is equal to the cost of 6 pens. What is the ratio of the cost of a book to the cost of a CD ?

A) 9 : 4
B) 4 : 9
C) 2 :3
D) 3 : 2
E) 2 : 1

Let 4 pens = 6 pencils = 12 cents, implying that each pen = 3 cents and that each pencil = 2 cents.
Cost of a book = cost of 6 3-cent pens = 6*3 = 18 cents.
Cost of a CD = cost of 4 2-cent pencils = 4*2 = 8 cents.
Resulting ratio:
18:8 = 9:4.

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Re: The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD  [#permalink]

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09 Jul 2018, 18:03
generis wrote:
selim wrote:
The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD is equal to the cost of 4 pencils and the cost of book is equal to the cost of 6 pens. What is the ratio of the cost of a book to the cost of a CD ?

A) 9 : 4
B) 4 : 9
C) 2 :3
D) 3 : 2
E) 2 : 1

The purposely NOT fancy way.

Everything is defined in terms of pens and pencils. Take the ratio of pens and pencils and define one in terms of the other.

(1) 4 pens cost the same as 6 pencils
4 PN = 6 PC
6 PC = 4 PN
PC = $$\frac{4}{6}=\frac{2}{3}$$PN

(2) One CD costs the same as 4 pencils
1CD = 4PC
CD cost in PNs?
From above, PC = $$\frac{2}{3}$$ PN
So 1CD = (4 *$$\frac{2}{3}$$PN)
1 CD = $$\frac{8}{3}$$ PN

(3) One book cost the same as 6 pens
1B = 6PN

(4) Book and CD cost in terms of PENS
1B = 6PN
1CD = $$\frac{8}{3}$$PN

(5) Ratio of book cost to CD cost?
$$\frac{B}{CD}=\frac{6}{(\frac{8}{3})}=(6*\frac{3}{8})=\frac{18}{8}=\frac{9}{4}$$

Given,

4 Pen = 6 Pencil
=> 1 Pen = 6/4 Pencil
=> 1 Pen = 3/2 Pencil ..... Equation 1

Also given,

1 Book = 6 Pen ...... Equation 2

And

1 CD = 4 Pencil ....... Equation 3

We need to find out below ratio

Book : CD

Substitute the value of Book and CD in terms of Pen and Pencil from equation 2 and 3 respectively

=> 6 Pen : 4 Pencil
=> 1 Pen : 4/6 Pencil
=> 1 Pen : 2/3 Pencil

Substitute the value of 1 Pen in terms of Pencil from equation 1

=> 3/2 Pencil : 2/3 Pencil
=> 9 Pencil : 4 Pencil
Cancel the Pencil form both the sides
=> 9 : 4

Hence, the expected ratio is 9:4.

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Re: The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD  [#permalink]

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17 Jul 2018, 16:44
selim wrote:
The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD is equal to the cost of 4 pencils and the cost of book is equal to the cost of 6 pens. What is the ratio of the cost of a book to the cost of a CD ?

A) 9 : 4
B) 4 : 9
C) 2 :3
D) 3 : 2
E) 2 : 1

We can let each pen cost 6 cents and each pencil cost 4 cents (notice that the cost of 4 pens is 24 cents and so is the cost of 6 pencils). So a CD would cost 4 x 4 = 16 cents and a book would cost 6 x 6 = 36 cents. Therefore, the ratio of the cost of a book to that of a CD is 36 : 16, or 9 : 4.

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Re: The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD &nbs [#permalink] 17 Jul 2018, 16:44
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