A house has decreased in value by 35% since it was purchased. If the current value is $286,000, what was the value when it was purchased?

To determine the original value of the house before the 35% decrease, we can use the following steps:

1. Let $ x $ represent the original purchase value of the house.
2. After a 35% decrease, the current value is 65% of the original value, since $ 100\% - 35\% = 65\% $.
3. Therefore, the current value is expressed as $ 0.65 \times x $.

We know the current value is $286,000, so we can set up the equation:
\[
0.65 \times x = 286,000
\]

To solve for $ x $, divide both sides of the equation by 0.65:
\[
x = \frac{286,000}{0.65}
\]

Now, let's calculate that.

\[
x = 440,000
\]

Thus, the house was originally purchased for **$440,000**.

Would you like more details or have any questions?

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Here are 5 related questions to consider:

1. If the house had decreased by 50%, what would the current value be?
2. What would be the value of the house after another 10% decrease from the current value?
3. How much money was lost due to the 35% decrease?
4. If the house were to regain its original value, by what percentage would it need to increase?
5. What would the current value be if the house decreased by 20% instead of 35%?

**Tip:** When dealing with percentage decreases, you can always express the remaining value as $ 100\% - \text{decrease percentage} $.

Learn how to determine the original value of a house that has decreased by 35%, with a current value of $286,000. This problem uses basic percentage decrease formulas and algebra, suitable for students in Grades 6-8.

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