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John Purchased 1375 large bottles at $1.89 per bottle and 69

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John Purchased 1375 large bottles at $1.89 per bottle and 69 [#permalink] New post 19 Feb 2014, 06:13
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John Purchased 1375 large bottles at $1.89 per bottle and 690 small bottles at $1.38 per bottle. What was the approximate average price paid per bottle?

A. $1.63
B. $1.64
C. $1.68
D. $1.72
E. $1.76

Can anyone please suggest a short and simple method for solving this question if possible.
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Feb 2014, 06:53, edited 1 time in total.
Renamed the topic and edited the question.
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Re: John Purchased 1375 large bottles at $1.89 [#permalink] New post 19 Feb 2014, 06:31
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First, see that 690 is approximately half of 1375.

So in total, we have two parts large bottles, and one part small bottle.

Now we can just add 1.89 + 1.89 + 1.38 and divide by 3 to get our answer.
If you do this calculation, we get exactly 1.72.

However, I would just add 1.9 + 1.9 + 1.4 = 5.2, and now divide by 3 to get 5.2/3 = 1.73
Because we rounded up (1.89 to 1.9 and 1.38 to 1.4) the answer is actually a bit less than 1.73, so the closest answer is 1.72, D.
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Re: John Purchased 1375 large bottles at $1.89 per bottle and 69 [#permalink] New post 19 Feb 2014, 07:33
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(1375*1.89+690*1.38)/(1375+690) = gives u the answer

A faster way to solve it is identifying that 1375 ~ 2x 690
Substituting this in the above equation u get - (2*1.89+1.38)/3 = 2*0.63+0.46=1.72 - Option (D)
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Re: John Purchased 1375 large bottles at $1.89 [#permalink] New post 19 Feb 2014, 08:10
farful wrote:
First, see that 690 is approximately half of 1375.

So in total, we have two parts large bottles, and one part small bottle.

Now we can just add 1.89 + 1.89 + 1.38 and divide by 3 to get our answer.
If you do this calculation, we get exactly 1.72.

However, I would just add 1.9 + 1.9 + 1.4 = 5.2, and now divide by 3 to get 5.2/3 = 1.73
Because we rounded up (1.89 to 1.9 and 1.38 to 1.4) the answer is actually a bit less than 1.73, so the closest answer is 1.72, D.

Thanks I realized that 690 is approximately half of 1375 but still ended up making a mistake.. Realized it through your explanation..
Re: John Purchased 1375 large bottles at $1.89   [#permalink] 19 Feb 2014, 08:10
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John Purchased 1375 large bottles at $1.89 per bottle and 69

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