A builder of custom homes reduced the price of a model by 10​%. If the new price is $ 585 comma 000 comma what was its original​ price? How much can be saved by purchasing the​ model?

Let's break down the problem.

### 1. Finding the Original Price
Let the original price be denoted by $ P $. The price was reduced by 10%, so the new price is 90% of the original price.

The equation is:
\[
0.9 \times P = 585,000
\]

To find $ P $, divide both sides of the equation by 0.9:
\[
P = \frac{585,000}{0.9} = 650,000
\]

So, the original price was **$650,000**.

### 2. Calculating the Savings
The savings are the difference between the original price and the new price:
\[
\text{Savings} = 650,000 - 585,000 = 65,000
\]

So, by purchasing the model at the reduced price, **$65,000** can be saved.

Would you like further details or have any questions?

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Here are some related questions for practice:
1. What would be the new price if the original price was reduced by 15% instead?
2. If the builder increased the price by 10%, what would the new price be?
3. How would the savings change if the price reduction was 12% instead of 10%?
4. If a different model is priced at $720,000 and reduced by 10%, what is the new price and savings?
5. How much would the original price be if the new price after a 20% reduction is $500,000?

**Tip:** When dealing with percentages, it's useful to remember that a reduction or increase is simply a multiplication factor applied to the original value.

Learn how to calculate the original price and savings when a builder reduces a custom home model's price by 10%. Get a detailed step-by-step solution, including finding the original price and determining savings of $65,000. Suitable for Grades 7-9.

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