If a store sells an item for $150 after a 10% discount, what was the original price?

To determine the original price of an item that is on sale for $150 after a 10% discount, it is essential to understand how discounts work.

When an item is sold at a discount, the selling price is equal to the original price minus the discount amount. In this case, if the item was sold for $150 after a 10% discount, we can express this mathematically. Let the original price be represented as ( P ). The discount is calculated as 10% of ( P ), which can be expressed as ( 0.10P ).

Thus, the price after the discount can be formulated as: [ P - 0.10P = 0.90P ] This means that the item is sold for 90% of its original price. According to the information, this selling price is $150, so we can write: [ 0.90P = 150 ]

To find the original price ( P ), we need to isolate ( P ) by dividing both sides of the equation by 0.90: [ P = \frac{150}{0.90} ]

Calculating this gives: [ P = 166.