To solve for the original price of the Chinese vase before the 20% hike, we need to work backwards from the final price.
Given:
- Final price after a 20% hike = 2000
- Hike percentage = 20%
Let the original price be [tex]\( x \)[/tex].
The relationship between the original price and the final price after a hike can be expressed as:
[tex]\[ \text{Final price} = \text{Original price} + (\text{Original price} \times \text{Hike percentage}) \][/tex]
[tex]\[ 2000 = x + (x \times \frac{20}{100}) \][/tex]
[tex]\[ 2000 = x + 0.2x \][/tex]
Now, combine like terms:
[tex]\[ 2000 = x(1 + 0.2) \][/tex]
[tex]\[ 2000 = 1.2x \][/tex]
To find the original price [tex]\( x \)[/tex], divide both sides by 1.2:
[tex]\[ x = \frac{2000}{1.2} \][/tex]
[tex]\[ x = 1666.67 \][/tex]
So, the original price of the Chinese vase was [tex]\( 1666.67 \)[/tex].
