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# On Monday, a person mailed 8 packages weighing an average

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Math Expert
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On Monday, a person mailed 8 packages weighing an average  [#permalink]

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13 Aug 2012, 05:57
5
13
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Difficulty:

5% (low)

Question Stats:

88% (01:55) correct 12% (02:40) wrong based on 1642 sessions

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On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of $$12\frac{3}{8}$$ pounds, and on Tuesday, 4 packages weighing an average of $$15\frac{1}{4}$$ pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

(A) $$13\frac{1}{3}$$

(B) $$13\frac{13}{16}$$

(C) $$15\frac{1}{2}$$

(D) $$15\frac{15}{16}$$

(E) $$16\frac{1}{2}$$

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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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13 Aug 2012, 05:57
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SOLUTION

On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of $$12\frac{3}{8}$$ pounds, and on Tuesday, 4 packages weighing an average of $$15\frac{1}{4}$$ pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

(A) $$13\frac{1}{3}$$

(B) $$13\frac{13}{16}$$

(C) $$15\frac{1}{2}$$

(D) $$15\frac{15}{16}$$

(E) $$16\frac{1}{2}$$

The total weight of 8 packages is $$8*12\frac{3}{8}=99$$ pounds;

The total weight of 4 packages is $$4*15\frac{1}{4}=61$$ pounds;

The average weight of all 12 packages is $$\frac{total \ weight}{# \ of \ packages}=\frac{99+61}{12}=13\frac{1}{3}$$.

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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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07 Sep 2012, 10:47
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Since the final average cannot be greater than $$15\frac{1}{4}$$, answers C, D and E are out.

We can use the property of weighted averages.
$$15\frac{1}{4}=15\frac{2}{8}$$, the distance between the two initial averages is almost 3.
Since the number of packages are in a ratio of 8:4 = 2:1, the differences between the final average and the initial averages are in a ratio 1:2.
So, the distance between $$12\frac{3}{8}$$ and the final average is almost 1, close to $$12\frac{3}{8}+1\approx{13}\frac{1}{4}$$.
The final answer should be close to $$13\frac{1}{4}$$.

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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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13 Aug 2012, 07:46
a person mailed 8 packages=99 pounds (total of all 8 packages)

and on Tuesday, 4 packages=61 pounds (total of all 4 packages)

total weight =99+61 =160 pounds

the average weight =160/(8+4) =option a
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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16 Aug 2012, 10:10
Bunuel wrote:
RESERVED FOR A SOLUTION.

Bunuel, had an off-topic request for you: Could you please post questions from non-OG sources as well? I'm not sure if that might breach a copyright arrangement bsaed on the source you use, and of course your comments on other's questions are supremely valuable for those of us subscribed to your daily updates - but if you could include occasional 700+ non-OG questions, would be much appreciated by your "followers"

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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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07 Sep 2012, 09:09
There must be something easy that i just don't get for me :
8*12(3/8) = 36 as you simplify the 8 between them. Therefore how do you manage to arrive at 99?

I guess it must be something different of spelling or something?

Thanks a lot for your help !
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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07 Sep 2012, 09:15
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Gmbrox wrote:
There must be something easy that i just don't get for me :
8*12(3/8) = 36 as you simplify the 8 between them. Therefore how do you manage to arrive at 99?

I guess it must be something different of spelling or something?

Thanks a lot for your help !

It's not 12 multiplied by 3/8. it's $$12\frac{3}{8}=\frac{12*8+3}{8}=\frac{99}{8}$$ (the same way as $$1\frac{1}{2}=\frac{3}{2}$$).
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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07 Sep 2012, 09:20
Thank you a lot bunuel, Ok after reviewing the official book, i now got it, it is a mix number, it does not exists in france so that's why. If anyone has difficulties to understand like me :

12(3/8) = 12+3/8 and not 12x(3/8).

Can be confusing.
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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24 Aug 2014, 23:54
I used weighted-averages to solve this as follows:

Let 12.375 be the lowest weight, therefore, (15.25 - 12.375) = 2.875, the difference in weights between the light and heavy packages.

Hence, the amount we need to add to 12.375 is:

(8x0 + 4x2.875)/(8+12) = 11.50 / 12 ~ 12/12 = 1 (Need to round final answer down a bit since I rounded numerator up)

Therefore, the average weight of all packages is approximately 12.375 + 1 = 13.375, since I need to round the numerator down, ans = 13.333, or A
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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15 Nov 2014, 01:55
1
I used ratio of packages, which is 2:1.
converted both to the same fractions, so
15 1/4 = 15 2/8

2x(12 3/8) + 1x( 15 2/8) = 24+15+ 6/8+2/8 = 39 and 8/8, 8/8 is also obviously 1. Could also be together 40 but that's not easily divisible with three and you know you're left with a remainder. Instead just:
39/3 + 1/3 = 13 and 1/3
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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20 Nov 2014, 02:08
2
Total weight on Monday $$= 8*12 + 8 * \frac{3}{8} = 96 + 3$$

Total weight on Tuesday $$= 4*15 + 4 * \frac{1}{4} = 60 + 1$$

Average of all days $$= \frac{96 + 60 + 4}{12} = 8 + 5 + \frac{4}{12} = 13\frac{1}{3}$$

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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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20 May 2016, 03:29
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Bunuel wrote:
SOLUTION

On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of $$12\frac{3}{8}$$ pounds, and on Tuesday, 4 packages weighing an average of $$15\frac{1}{4}$$ pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

(A) $$13\frac{1}{3}$$

(B) $$13\frac{13}{16}$$

(C) $$15\frac{1}{2}$$

(D) $$15\frac{15}{16}$$

(E) $$16\frac{1}{2}$$

Solution:

To solve this question we can use the weighted average equation.

Weighted Average = (Sum of Weighted Terms) / (Total Number of Items)

We'll first determine the sum (numerator). We see that on the first day we had 8 items that averaged 12 3/8 pounds. We don't know the weights of the individual packages, but we can determine that the sum of all 8 packages is:

Sum of first day's packages = 8 x 12 3/8 = 99 pounds

Similarly, the sum of the second day's packages is:

Sum of second day's packages = 4 x 15 ¼ = 61

We now can use the weighted average equation to find the average weight of the 12 packages:

Weighted Average = (99 + 61) / 12

Weighted Average = 160 /12

Weighted Average = 13 1/3

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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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20 Jul 2016, 11:55
The total weight of packages on Monday = 12 $$\frac{3}{8}$$ * 8 = 99 pounds

The total weight of packages on tuesday = 15 $$\frac{1}{4}$$ * 4 = 61 pounds

Average = Total weight / Number of packages = $$\frac{(99+61)}{12}$$ = 13 $$\frac{1}{3}$$ pounds
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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20 Jul 2016, 14:25
(2*12 3/8)+(1*15 1/4)=40 pounds
40/3=13 1/3 pounds average
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On Monday, a person mailed 8 packages weighing an average  [#permalink]

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15 Dec 2016, 14:15
This Question is giving us mean of two data and asking us for the combined average.

Using $$Mean = Sum/#$$

Sum(8) = $$\frac{99}{8}*8=99$$
Sum(4)=$$\frac{61}{4}*4=61$$

Hence combined average =$$\frac{99+61}{12}= \frac{40}{3}$$
Hence A

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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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28 Jul 2017, 15:02
Using the weighted average formula =
weight of x (x) + weight of y (y) = weight of x and y (x+y)

In this situation, x =8, weighting of x = 12 3/8; y = 4, weighting of y = 15 1/4

substitute in the formula to find
99 + 61 = weight of x and y (8 +4)
99 + 61 = weight of x and y (12)
(99+61)/12 = weight of x and y
= 13 1/3
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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Re: On Monday, a person mailed 8 packages weighing an average   [#permalink] 09 Sep 2018, 16:40
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