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The weight of every type A widget is the same, the weight of

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The weight of every type A widget is the same, the weight of [#permalink] New post 01 Jan 2008, 18:27
The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 8 type A widgets is equal to the weight of 3 type B widgets, and the weight of 5 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget?


12/23
21/40
2/3
77/96
10/7

Please explain.

[spoiler]OA is D[/spoiler]
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Re: Ratios [#permalink] New post 02 Jan 2008, 02:35
D

8A=3B; 5B=7C; r=(A+B)/(B+C) ?

B=8/3A; C=5/7B=5/7*8/3A

r=(A+B)/(B+C)=(A+8/3A)/(8/3A+5/7*8/3A)=(11/3)/(8/3*12/7)=77/96
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Re: Ratios [#permalink] New post 02 Jan 2008, 06:02
AVakil wrote:
The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 8 type A widgets is equal to the weight of 3 type B widgets, and the weight of 5 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget?


12/23
21/40
2/3
77/96
10/7

Please explain.

[spoiler]OA is D[/spoiler]


8A=3B AND 5B=3C...let's put everything in terms of B, so ... A=3/8*B and C=5/7*B, thus (A+B)/B+C=11/8*7/12=77/96. OA must be D
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Re: Ratios [#permalink] New post 02 Jan 2008, 08:42
A real easy way that doesn't involve any division:

A:B = 3:8
B:C = 7:5

therefore
A:B:C
= 3*7:7*8:5*8
=21:56:40

therefore (A+B)/(B+C) = (21+56)/(56+40) = 77/96
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Re: Ratios [#permalink] New post 02 Jan 2008, 09:20
i ended up with 77/96 as well, so answer choice D
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Re: Ratios [#permalink] New post 02 Jan 2008, 11:04
buffdaddy wrote:
A real easy way that doesn't involve any division:

A:B = 3:8
B:C = 7:5

therefore
A:B:C
= 3*7:7*8:5*8
=21:56:40

therefore (A+B)/(B+C) = (21+56)/(56+40) = 77/96


Holy moly. By far the best method I have seen. Does this work for all problems involving ratios?
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Re: Ratios [#permalink] New post 02 Jan 2008, 11:37
buffdaddy wrote:
A real easy way that doesn't involve any division:

A:B = 3:8
B:C = 7:5

therefore
A:B:C
= 3*7:7*8:5*8
=21:56:40

therefore (A+B)/(B+C) = (21+56)/(56+40) = 77/96


very, very slick. I love this approach 8-)
Re: Ratios   [#permalink] 02 Jan 2008, 11:37
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