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The original price of an item is $1.40. Lenny bought 4 items at full p
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16 Sep 2021, 09:36
16 Sep 2021, 09:36
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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
A. $1.01
B. $1.06
C. $1.10
D. $1.12
E. $1.18
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Re: The original price of an item is $1.40. Lenny bought 4 items at full p
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16 Sep 2021, 10:08
16 Sep 2021, 10:08
Carcass 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
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: C
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General Discussion
Re: The original price of an item is $1.40. Lenny bought 4 items at full p
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16 Sep 2021, 11:04
16 Sep 2021, 11:04
1
using weighted average formula
avg= [(4x1.4)+(0.8x1.4x5)+(0.6x1.4x5)]/14
solving above,
avg= 1.1
Answer: C
avg= [(4x1.4)+(0.8x1.4x5)+(0.6x1.4x5)]/14
solving above,
avg= 1.1
Answer: C
