An item, which is regularly $4.60, is on sale for one-fourth off. What is the sale price?

Solution:

Goods are often sold on the discounted price and the discounts are always given on the marked price of the goods or items. 

If the marked price of an item is MP and the discount or the rebate offered on the item is R% then the price at which the customer will finally purchasing the item will be calculated as shown below:

Discount = R % of the Marked price = (R/100) × Marked Price(MP)

Therefore the sales price or the price at which the customer finally purchases the item is given by the following expression:

Sales/Purchase Price = Marked Price (MP) - (R/100) × Marked Price(MP)

= (1 - R/100) × Marked Price(1)

The Marked price of the item as per the problem statement is = $4.60

The offer available to the customer is one-fourth off which means 25% discount on the marked price. Therefore the discount is:

Discount = 25% of the Marked Price

= 25/100 × 4.60

= (1/4) × 4.60

= $ 1.25

Sales price or the price paid by the customer = 4.60 - 1.15 = $ 3.45

Alternatively the sales or the purchase price could be directly calculated using equation (1) above i.e.

Purchase or sales Price = (1 - R/100) × Marked Price

= (1 - 25/100) × 4.60

= 0.75 × 4.60

= $3.45

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An item, which is regularly $4.60, is on sale for one-fourth off. What is the sale price?

Summary:

The sales price of an item with a marked price of $4.60 and a discount of one-fourth off on the marked price is $3.45.