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The original price of an item is $1.40. Lenny bought 4 items at full
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12 May 2017, 05:17
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64% (01:38) correct 36% (02:25) wrong based on 75 sessions
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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?
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: The original price of an item is $1.40. Lenny bought 4 items at full
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12 May 2017, 05:23
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
Re: The original price of an item is $1.40. Lenny bought 4 items at full
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16 May 2017, 06:06
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
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16 May 2017, 06:45
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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
Re: The original price of an item is $1.40. Lenny bought 4 items at full
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16 May 2017, 07:47
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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Abhishek....
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Re: The original price of an item is $1.40. Lenny bought 4 items at full
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19 May 2017, 06:17
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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