# Comparing discounts

In this lesson, we consider two product choices with their list prices and discount rates. We find the actual discounts and sale prices and after comparing them we decide which is the best buy. This involves as we see, comparing discounts of products (usually two at a time) to decide which one is a better buy.

**Rules to compare discounts and decide which is a better buy.**

First consider the marked or list prices of products.

Then consider the rates of discount for those products.

To find the actual discounts, multiply the discount rates by the marked prices.

To find the sale prices, subtract the actual discounts from the marked prices.

Compare the discounts and the sale prices and decide which product is a better buy.

Marked price (M.P.) of A = $200; Discount = 25% off; M.P. of B = $220; Discount = 30% off. Of the two, A and B, which is a better buy?

### Solution

**Step 1:**

M.P. of A = $200; Discount rate of A = 25%

Discount = 0.25 × 200 = $50;

Sale price of A = $200 − $50 = $150

**Step 2:**

M.P. of B = $220; Discount rate of B = 30%

Discount = 0.3 × 220 = $66

Sale price of B = $220 − $66 = $154

**Step 3:**

Comparing the discounts and final sale prices, product A is the better buy as it is cheaper compared to product B ($150 < $154)

Trader P sells an item for $400 at 25% off; Trader Q sells the same item for $425 at 30% off. Which is a better buy?

### Solution

**Step 1:**

Discount of trader P = 25% of $400 = 0.25 × 400 = $100

Sale price of trader P = $400 − $100 = $300

**Step 2:**

Discount of trader Q = 30% of $425 = 0.3 × 425 = $127.50

Sale price of trader Q = $425 − $127.50 = $297.50

**Step 3:**

Since $297.50 < $300, purchasing from Trader Q is a better buy.