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The original price of an item is $1.40. Lenny bought 4 items at full

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The original price of an item is $1.40. Lenny bought 4 items at full [#permalink]

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New post 12 May 2017, 04:17
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Question Stats:

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The original price of an item is $1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item?

A. $1.01
B. $1.06
C. $1.10
D. $1.12
E. $1.18
[Reveal] Spoiler: OA

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Re: The original price of an item is $1.40. Lenny bought 4 items at full [#permalink]

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New post 12 May 2017, 04:23
Bunuel wrote:
The original price of an item is $1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item?

A. $1.01
B. $1.06
C. $1.10
D. $1.12
E. $1.18


Total Price Lenny paid = 4*1.40 + 5* 1.4 *0.8 + 5*1.4*0.6 = 1.4*(4+4+3) =1.4*11
Average price paid per item = 1.4 *11/ 14 = $1.10

[Reveal] Spoiler:
Answer C

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Re: The original price of an item is $1.40. Lenny bought 4 items at full [#permalink]

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New post 12 May 2017, 04:25
4x 1.40
5x 1.12 (20% off)
5x 0.84 (40% off)
Total of 15.40 for 14 items. 15.40/14= 1.1
C
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Re: The original price of an item is $1.40. Lenny bought 4 items at full [#permalink]

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New post 16 May 2017, 05:06
The original price of an item is $1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item?

A. $1.01
B. $1.06
C. $1.10
D. $1.12
E. $1.18

Original price = 1.40
4 items bought at full price = 4 x 1.40 = 5.60
5 items bought at a 20% discount = 5 x ( 80% of 1.40) = 5 x (\(\frac{80}{100}\) x 1.40) = 5.60
5 items bought at a 40% discount = 5 x (60% of 1.40) = 5 x (\(\frac{60}{100}\) x 1.40) = 4.20

Total number of items = 5+5+4 = 14
Total price of 14 items = 5.60 + 5.60 + 4.20 = 15.40
Average price = \(\frac{15.40}{14}\) = $1.10
Answer C....

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Re: The original price of an item is $1.40. Lenny bought 4 items at full [#permalink]

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New post 16 May 2017, 05:45
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Bunuel wrote:
The original price of an item is $1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item?

A. $1.01
B. $1.06
C. $1.10
D. $1.12
E. $1.18


We can also apply the weighted averages formula:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

So, average price paid = (proportion of items bought at full price)(full price) + (proportion of items bought at 20% off)(price at 20% off) + (proportion of items bought at 40% off)(price at 40% off)

The TOTAL number of purchases = 4 + 5 + 5 = 14
Full price = $1.40
Price with 20% discount = (0.8)($1.40)
Price with 40% discount = (0.6)($1.40)

So, average price paid = (4/14)($1.40) + (5/14) (0.8)($1.40) + (5/14) (0.6)($1.40)

IMPORTANT: Notice that, when $1.40 is multiplied by each fraction with 14 in the denominator, the product is a nice number to work with.
For example, (4/14)($1.40) = (4)($0.10) = $0.40
And (5/14) (0.8)($1.40) = (5)(0.8)($0.10) = $0.40
And (5/14) (0.6)($1.40) = (5)(0.6)($0.10) = $0.30

So, we get: average price paid = $0.40 + $0.40 + $0.30
= $1.10

Answer:
[Reveal] Spoiler:
C


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Re: The original price of an item is $1.40. Lenny bought 4 items at full [#permalink]

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New post 16 May 2017, 06:47
Bunuel wrote:
The original price of an item is $1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item?

A. $1.01
B. $1.06
C. $1.10
D. $1.12
E. $1.18


Cost price of the items is = (1.40*4) + (5*80%*1.40) + (5*60%*1.40)

Cost price of the items is = 5.6 + 5.6 + 4.2

Cost price of the items is = 15.4

He bought a total of 14 items, so average price is 1.10

Thus, answer must be (C) $1.10
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Re: The original price of an item is $1.40. Lenny bought 4 items at full [#permalink]

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New post 19 May 2017, 05:17
Bunuel wrote:
The original price of an item is $1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item?

A. $1.01
B. $1.06
C. $1.10
D. $1.12
E. $1.18


Since the original price of an item is 1.40, the price with a 20% discount is 0.8 x 1.40 = $1.12 and the price with a 40% discount is 0.6 x 1.40 = $0.84.

Since 4 items were purchased at full price, the total spent on those items was 1.4 x 4 = $5.60. Since 5 items were purchased at a 20% discount, the total spent on those items was 5 x 1.12 = $5.60. Finally, since 5 items were purchased at a 40% discount, the total spent on those items was 5 x 0.84 = $4.20.

The average price per item was:

(5.6 + 5.6 + 4.2)/14 = 15.4/14 = $1.10.

Answer: C
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Re: The original price of an item is $1.40. Lenny bought 4 items at full   [#permalink] 19 May 2017, 05:17
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