The original price of a certain Television set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the television Set, which of the following represents the price of the television set after the two successive discounts?
A: P(1 - 0.03x + 0.02x^2)
B: P(1 - 0.03x + 0.0002x^2)
C: P(1 - 0.3x + 0.002x^2)
D: P(1 - 2x^2)
E: P(1 - 3x + 2x^2)
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The original price of a certain Television set is discounted
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alanforde800Maximus
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Let P = 100 and x = 10, implying that 2x = 20.alanforde800Maximus wrote:The original price of a certain Television set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the television Set, which of the following represents the price of the television set after the two successive discounts?
A: P(1 - 0.03x + 0.02x^2)
B: P(1 - 0.03x + 0.0002x^2)
C: P(1 - 0.3x + 0.002x^2)
D: P(1 - 2x^2)
E: P(1 - 3x + 2x^2)
Price after an x% discount = 100 - (10% of 100) = 100 - 10 = 90.
Price after a 2x% discount = 90 - (20% of 90) = 90 - 18 = 72.
The correct answer must yield a resulting price of $72 when x=10.
Only B works:
100(1 - 0.03*10 + 0.0002*10²) = 100(1 - 0.3 + 0.02) = 100(0.72) = 72.
The correct answer is B.
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You can solve this problem with number plugging.
Say the original price was $10 and x = 50. Then after the first reduction, the price would become $5 and after the second reduction of 2*50 = 100%, the price would become $0.
Now, since P is not zero, then the expression in the brackets must be must be zero for x = 50. Only answer choice B works.
Regards!
Say the original price was $10 and x = 50. Then after the first reduction, the price would become $5 and after the second reduction of 2*50 = 100%, the price would become $0.
Now, since P is not zero, then the expression in the brackets must be must be zero for x = 50. Only answer choice B works.
Regards!
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We can create the expression:alanforde800Maximus wrote:The original price of a certain Television set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the television Set, which of the following represents the price of the television set after the two successive discounts?
A: P(1 - 0.03x + 0.02x^2)
B: P(1 - 0.03x + 0.0002x^2)
C: P(1 - 0.3x + 0.002x^2)
D: P(1 - 2x^2)
E: P(1 - 3x + 2x^2)
P(1 - x/100)(1 - 2x/100)
P(1 - 3x/100 + 2x^2/10000)
P(1 - 0.03x + 0.0002x^2)
Answer: B
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