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A woman sold 100 oranges at $12.10, some at the rate of 3

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A woman sold 100 oranges at $12.10, some at the rate of 3 [#permalink] New post 26 Jul 2010, 07:39
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Question Stats:

66% (03:09) correct 34% (03:05) wrong based on 175 sessions
A woman sold 100 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 7 for 85 cents. How many were sold at the first rate?

A. 45
B. 21
C. 9
D. 15
E. 12
[Reveal] Spoiler: OA

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Re: Oranges sold at different rates [#permalink] New post 26 Jul 2010, 08:58
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This can be solved like a classical mixture problem but numbers are awkward to deal with.

It's easier to just look at the answer choices. You know that a multiple of 3 oranges has to be sold at the first rate, and a multiple of 7 at the second rate. You simple subtract the answer choices for the first rate from 100 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 7.

100 - 45 = 55 => not a multiple of 7 so exclude
100 - 21 = 79 => not a multiple of 7 so exclude
100 -9 = 91 => a multiple of 7 so keep
100 - 15 = 85 => not a multiple of 7 so exclude
100 - 12 = 88 => not a multiple of 7 so exclude

Hence, answer choice 9 is correct.
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Re: Oranges sold at different rates [#permalink] New post 29 Feb 2012, 09:03
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\frac{35}{3}x+\frac{85}{7}(100-x)=1210

solve and you'll get x = 9

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Re: Oranges sold at different rates [#permalink] New post 15 Mar 2012, 20:18
\frac{35}{3}x+\frac{85}{7}(100-x)=1210

Can you pls explain the Right hand side of equation.
Won't it be 12.10

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Re: Oranges sold at different rates [#permalink] New post 15 Mar 2012, 21:45
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GMATD11 wrote:
\frac{35}{3}x+\frac{85}{7}(100-x)=1210

Can you pls explain the Right hand side of equation.
Won't it be 12.10


The equation equates the total selling price. He gets $12.10 i.e. 1210 cents.
If he sold x oranges for 35/3 cents and (100-x) for 85/7 cents, this is a total of
(35/3) * x + (85/7) * (100-x) cents. You equate cents to cents.

Also, you can use the weighted average formula here:

w1/w2 = (85/7 - 121/10)/(121/10 - 35/3) = 9/91

Total 9+91 is 100. So he sells 9 oranges at 35 for 3 and 91 oranges at 85 for 7.

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Re: Oranges sold at different rates [#permalink] New post 16 Aug 2012, 23:47
GMATD11 wrote:
\frac{35}{3}x+\frac{85}{7}(100-x)=1210

Can you pls explain the Right hand side of equation.
Won't it be 12.10


Hi,

Because we are taking all the values in cents so we have converted $12.10 into cents which is 1210 cents.
as 1 cent =0.01 Dollar

Hope this helps.

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Re: A woman sold 100 oranges at $12.10, some at the rate of 3 [#permalink] New post 29 Sep 2013, 07:23
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Re: A woman sold 100 oranges at $12.10, some at the rate of 3 [#permalink] New post 01 Oct 2013, 04:31
for such question need a will power to take on some random complicated numbers. i derived the equation but goofed up with the numbers :(

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Re: A woman sold 100 oranges at $12.10, some at the rate of 3   [#permalink] 01 Oct 2013, 04:31
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