Carcass wrote:
A store calls the original price of an item the X-level price. The store reduces the X-level price of an item by 30%, resulting in what the store calls the Y-level price of the item. The store then reduces the Y-level price of the item by 20%, resulting in what the store calls the Z-level price of the item. The Z-level price of the item is less than $ 49. Which of the following statements must be true?
Indicate all such statements.
A. The X-level price of the item is less than $ 86.00.
B. When the Z-level price of the item is subtracted from the Y-level price of the item, the result is less than $ 16.00.
C. The Y-level price of the item is a percent greater than the Z-level price of the item, where \(0 < a < 30\)
X-level price = \(x\)
Y-level price = \(0.7x\)
Z-level price = \((0.8)(0.7x) = 0.56x\)
Now,
\(0.56x < 49\)
\(x < 87.5\)
A. The X-level price of the item is less than $ 86.00 - NOIt is less than $87.50, but how much - we have no idea!
It might be $87 or $80
B. When the Z-level price of the item is subtracted from the Y-level price of the item, the result is less than $ 16.00 - YES\(0.70x - 0.56x = 0.14x = 0.14(87.50) =\) $12.25
C. The Y-level price of the item is \(a\) percent greater than the Z-level price of the item, where \(0 < a < 30\) - YES\(\frac{Y}{Z} = \frac{(0.70x)}{(0.56x)} = 1.25\), which means it is \(25\)% greater
Hence, option B and C