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01 Oct 2019, 02:55
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D
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Difficulty:
35%
(medium)
Question Stats:
77% (02:23) correct
23%
(02:59)
wrong
based on 69
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When a popular brand of CD player is priced at $300 per unit, a store sells 15 units per week. Each time the price is reduced by $10, however, the sale increases by two per week. What selling price will result in weekly revenues of $7000? (Assume that the price is reduced by exactly $10 each time)
A. $175
B. $180
C. $190
D. $200
E. $210
A. $175
B. $180
C. $190
D. $200
E. $210
01 Oct 2019, 04:55
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Bunuel
Revenue = number * price of each
Let the number of times price decreased by $10 = x
—> New price = \(300 - 10x\)
& Number of items sold = \(15 + 2x\)
—> \(7000 = (300 - 10x)*(15 + 2x)\)
—> \(700 = (30 - x)(15 + 2x)\)
—> \(2x^2 - 45x + 250 = 0\)
—> \(2x^2 - 20x - 25x + 250 = 0\)
—>\((2x - 25)(x - 10) = 0\)
—> \(x = 10\)
New Price = 300 - 10*10 = 200
IMO Option D
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07 Oct 2019, 20:03
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Bunuel
If the price of the CD player is 300 - 10(10) = 200 dollars, then 15 + 2 x 10 = 35 units are sold. We see that the revenue will be exactly 200 x 35 = 7000 dollars; so the price must be 200 dollars.
Alternate Solution:
Let n denote the number of $10 reductions in the price of the CD player. Then, the price of the CD player is (300 - 10n), and the number of units sold is (15 + 2n) per week. We can create the following equation:
(300 - 10n)(15 + 2n) = 7000
4500 + 600n - 150n - 20n^2 = 7000
450 + 60n - 15n - 2n^2 = 700
450 + 45n - 2n^2 = 700
2n^2 - 45n + 250 = 0
(2n - 25)(n - 10) = 0
n = 25/2 or n = 10
Since we are told that the price is reduced by exactly $10 each time, n must be an integer, and thus, n = 10. So, the price that results in a $7000 weekly revenue is 300 - 10n = 300 - 10(10) = $200.
Answer: D
