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# Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, wei

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Math Expert
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Posts: 51185
Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, wei  [#permalink]

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25 Mar 2018, 23:34
00:00

Difficulty:

25% (medium)

Question Stats:

87% (01:46) correct 13% (02:04) wrong based on 37 sessions

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Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, weighing an average of 15.25 kilograms, are shipped to the same location. What is the average weight, in kilograms, of the 20 boxes shipped to the location?

(A) 13
(B) 13.25
(C) 14
(D) 14.25
(E) 15

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Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, wei  [#permalink]

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26 Mar 2018, 00:12
Bunuel wrote:
Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, weighing an average of 15.25 kilograms, are shipped to the same location. What is the average weight, in kilograms, of the 20 boxes shipped to the location?

(A) 13
(B) 13.25
(C) 14
(D) 14.25
(E) 15

We know 1.25 = $$\frac{5}{4}$$. Hence $$\frac{5}{4}*8 = 10$$ and $$\frac{5}{4}*12 = 15$$

Average = $$\frac{(14 - 1.25)*8 + (14 + 1.25)*12}{20} = \frac{14*20 - 10 + 15}{20} = 14 + \frac{5}{20} = 14.25$$

Therefore, the average of 20 boxes shipped is 14.25(Option D)
P.S In order to solve problems such as these, it is important to identify a pattern to reduce unnecessary calculations.
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Re: Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, wei  [#permalink]

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26 Mar 2018, 00:46
pushpitkc wrote:
Bunuel wrote:
Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, weighing an average of 15.25 kilograms, are shipped to the same location. What is the average weight, in kilograms, of the 20 boxes shipped to the location?

(A) 13
(B) 13.25
(C) 14
(D) 14.25
(E) 15

We know 1.25 = $$\frac{5}{4}$$. Hence $$\frac{5}{4}*8 = 10$$ and $$\frac{5}{4}*12 = 15$$

Average = $$\frac{(14 - 1.25)*8 + (14 + 1.25)*12}{20} = \frac{14*20 - 10 + 15}{20} = 14 + \frac{5}{20} = 14.25$$

Therefore, the average of 20 boxes shipped is 14.25(Option D)

P.S In order to solve problems such as these, it is important to identify a pattern to reduce unnecessary calculations.

Great way to simplify this pushpitkc,

Another way to look at it is -

$$12.75 = 12 \frac{3}{4} improper fraction ... (12*4 +3 )/4 = 51/4$$
$$15.25 = 15 \frac{1}{4} = 61/4$$

Numerator is : $$\frac{51}{4}* 8 + \frac{61}{4}*3 = 50*2 + 60*3 + 2 + 3 = 285$$

On dividing by 20 .. which is 10 * 2

Divide by 2 first and move decimals point one to the left.

Hence $$285 / 2 = 142.5 / 10 = 14.25$$

Hence Option (D) is correct.

Always try to simplify the calculations as much as possible...

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Re: Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, wei  [#permalink]

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26 Mar 2018, 08:28
Bunuel wrote:
Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, weighing an average of 15.25 kilograms, are shipped to the same location. What is the average weight, in kilograms, of the 20 boxes shipped to the location?

(A) 13
(B) 13.25
(C) 14
(D) 14.25
(E) 15

$$\frac{(8*12 + 8*0.75) + (12*15 + 12*0.25)}{(8 + 20)}$$

$$\frac{96 + 6 + 180 + 3}{20}$$

$$\frac{285}{20}$$

$$14.25$$

(D)
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Re: Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, wei  [#permalink]

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28 Mar 2018, 09:34
Bunuel wrote:
Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, weighing an average of 15.25 kilograms, are shipped to the same location. What is the average weight, in kilograms, of the 20 boxes shipped to the location?

(A) 13
(B) 13.25
(C) 14
(D) 14.25
(E) 15

The total weight of the 20 boxes is:

12.75 x 8 + 15.25 x 12 = 102 + 183 = 285 kg

The average is 285/20 = 14.25 kg.

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Re: Eight boxes, weighing an average of 12.75 kilograms, and 12 boxes, wei &nbs [#permalink] 28 Mar 2018, 09:34
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