A shop gives a 10% discount on all items. Find the original price of each item based on the sale price. 1. 112.50

To find the original price of an item after a 10% discount has been applied, we can use the following method:

Let the original price of the item be $ x $.

Since the shop gives a 10% discount, the sale price is 90% of the original price:

\[
\text{Sale Price} = 0.9x
\]

We are given that the sale price is 112.50, so:

\[
0.9x = 112.50
\]

To find the original price $ x $, divide both sides of the equation by 0.9:

\[
x = \frac{112.50}{0.9}
\]

\[
x = 125
\]

So, the original price of the item is **$125.00**.

Would you like any more details or explanations on this? 

Here are five related questions:

1. How do you calculate the sale price if you know the original price and the discount percentage?
2. What is the final price of an item if a 10% tax is added after the 10% discount?
3. How would the original price change if the discount were 15% instead of 10%?
4. What is the relationship between the discount percentage and the sale price?
5. How can you calculate the percentage discount if you know the original and sale prices?

**Tip:** Always double-check the percentage calculations by considering whether the final value makes sense compared to the original context.

Learn how to find the original price of an item after a 10% discount based on a sale price of $112.50. This problem covers calculating percentages and discounts, suitable for middle school students.

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