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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]

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New post Updated on: 19 Feb 2014, 07:53
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Question Stats:

67% (02:28) correct 33% (02:40) wrong based on 153 sessions

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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.

Originally posted by aks456 on 19 Feb 2014, 07:13.
Last edited by Bunuel on 19 Feb 2014, 07:53, 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]

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New post 19 Feb 2014, 07:31
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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]

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New post 19 Feb 2014, 08:33
1
(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]

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New post 19 Feb 2014, 09:10
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..
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Re: John Purchased 1375 large bottles at $1.89 per bottle and 69  [#permalink]

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New post 17 Sep 2018, 12:07
aks456 wrote:
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.



Simple math problem. it takes large amount of time.

i do agree with taking aproximations of 2:1 and adding in 2:1 ratio. and divide by 3 to get faster results.
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Re: John Purchased 1375 large bottles at $1.89 per bottle and 69  [#permalink]

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New post 18 Sep 2018, 18:51
aks456 wrote:
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


Average = (1375 x 1.89 + 690 x 1.38)/(1375 + 690)

Average = 3550.95/2065

Average ≈ 1.72

Alternate solution:

Notice that had 1380 large bottles been purchased, it would be exactly twice the number of small bottles purchased. In that case, the average would be 1/3 of the way (i.e., the difference between 1.89 and 1.38) from 1.89 and 2/3 of the way from 1.38.

Since the difference between 1.89 and 1.38 is 0.51 and 1/3 of it is 0.17, then the average is 0.17 less than 1.89, or 0.34 more than 1.38. Either way, the average would be 1.72. Since 1375 large bottles were purchased, the average would not be 1.72, but it will be very close to it since 1375 is very close to 1380.

Answer: D
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Re: John Purchased 1375 large bottles at $1.89 per bottle and 69  [#permalink]

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New post 21 Sep 2018, 22:31
We are asked for the approximate average price per bottle, which means that we should look to round off certain values. However, the answers are close together, so we do not want to run the risk of doing too much rounding, otherwise we might select one of the incorrect answers. To avoid that outcome, we should keep the prices as is and consider the number of bottles purchased.

If we were to double the number of small bottles, then we would end up with \(690 \times 2 = 1380\). This is almost exactly the number of large bottles, so we have an approximate ratio of large bottles to small bottles in the ratio of \(2:1\).

With the ratio, the average will be the same regardless of the number of bottles involved, so we can calculate assuming that there are just 2 large bottles and 1 small bottle.

The average price paid per bottle would be

\(Average=\frac{(2×1.89)+(1×1.38)}{2+1}=\frac{5.16}{3}=1.72\)

The final answer is .
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Re: John Purchased 1375 large bottles at $1.89 per bottle and 69 &nbs [#permalink] 21 Sep 2018, 22:31
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John Purchased 1375 large bottles at $1.89 per bottle and 69

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