A house had decreased in value by 35% since it was purchased . If the value now is 208,000, what was the value?
The correct answer and explanation is:
To find the original value of the house, we need to reverse the 35% decrease. The house is now worth 208,000, and that represents 65% (100% – 35%) of its original value.
We can express this as: Original Value=Current Value1−Percentage Decrease\text{Original Value} = \frac{\text{Current Value}}{1 – \text{Percentage Decrease}}
Substitute the given values into the equation: Original Value=208,0000.65\text{Original Value} = \frac{208,000}{0.65} Original Value=320,000\text{Original Value} = 320,000
Thus, the house was originally worth 320,000.
Explanation
- Understanding the problem: The house has decreased in value by 35%. This means that 65% of the original value is the current price.
- Setting up the formula:
We know that the current value represents 65% of the original value. To find the original value, we divide the current value by 0.65. This is because 65% in decimal form is 0.65. - Calculating the original value:
When we divide the current value (208,000) by 0.65, we get 320,000. This means that the house was originally worth 320,000 before the decrease in value. - Conclusion: The original value of the house was 320,000. After a decrease of 35%, its current value is 208,000. This method of calculation is helpful in determining the original price when a percentage decrease is known.