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11 Feb 2025, 06:51
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
0% (00:00) correct
100% (02:35) wrong based on 1 sessions
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A certain bookstore sells only paperbacks and hardbacks. Each of the 200 paperbacks in stock sells for a price between $8 and $12, and each of the 100 hardbacks in stock sells for a price between $14 and $18.
Quantity A
The average price of the books in stock at the bookstore
Quantity B
$9.99
Quantity A
The average price of the books in stock at the bookstore
Quantity B
$9.99
14 Feb 2025, 08:40
Kudos
Bookmarks
OE
Because there are twice as many paperbacks as hardbacks in stock, the overall average price will be closer to the price of the paperbacks than the price of the hardbacks. However, the fact that the problem gives price ranges instead of prices complicates matters a bit. Calculate the lowest possible overall average and the highest possible overall average to see whether that average can be both lower and higher than $9.99.
To calculate the lowest possible overall average, assume the lowest price for all paperbacks and all hardbacks ($8 and $14, respectively). Note that there are twice as many paperbacks as hardbacks, which essentially double-weights the $8:
\(\frac{200($8)+100($14)}{200+100}=\frac{2($8)+1($14)+}{3}=\frac{$30}{3}=$10\)
This minimum average price is already greater than $9.99, so the maximum average price would also be greater and there is no need to calculate it.
Quantity A is greater.
Because there are twice as many paperbacks as hardbacks in stock, the overall average price will be closer to the price of the paperbacks than the price of the hardbacks. However, the fact that the problem gives price ranges instead of prices complicates matters a bit. Calculate the lowest possible overall average and the highest possible overall average to see whether that average can be both lower and higher than $9.99.
To calculate the lowest possible overall average, assume the lowest price for all paperbacks and all hardbacks ($8 and $14, respectively). Note that there are twice as many paperbacks as hardbacks, which essentially double-weights the $8:
\(\frac{200($8)+100($14)}{200+100}=\frac{2($8)+1($14)+}{3}=\frac{$30}{3}=$10\)
This minimum average price is already greater than $9.99, so the maximum average price would also be greater and there is no need to calculate it.
Quantity A is greater.
