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Best Buys with Discount

This lesson shows how to determine the best buy when items are discounted. Students learn to calculate the sale price from a percent discount, convert sale prices to unit prices, and compare products fairly, since the item with the bigger percent discount is not always the cheaper option per unit.

What does "best buy with discount" mean?

When stores put items on sale, the discount is usually shown as a percent off the original price. A "best buy" question asks which product gives you the most for your money once that discount is applied. This builds directly on comparing unit price and best buys, except now the price you compare is not the original sticker price, it is the discounted price.

The tricky part is that the item with the larger percent discount is not always the cheaper choice. A small package with a 40% discount can still cost more per unit than a large package with only a 10% discount. To answer these problems correctly, you always need to work out the actual sale price first, then find the unit price.

Step 1: Calculate the sale price

To turn a percent discount into a dollar amount, subtract the discount rate from 1 and multiply by the original price:

$ P_{sale} = P_{original} \times (1 - d) $

Here $ P_{original} $ is the price before the discount, $ d $ is the discount rate written as a decimal (so 20% becomes 0.20), and $ P_{sale} $ is the price you actually pay.

For example, a $15 item marked 20% off costs $ 15 \times (1 - 0.20) = 15 \times 0.80 = 12 $ dollars.

Step 2: Turn each sale price into a unit price

Once you know the sale price, divide it by the quantity, weight, or number of items in the package:

$ U = \dfrac{P_{sale}}{q} $

where $ q $ is the amount you get (ounces, count, liters, and so on). The item with the smaller unit price is the better buy, as long as the units being compared are the same.

Worked example 1: Two sizes of the same product

A 12-ounce bottle of juice normally costs $3.00 and is on sale for 25% off. A 20-ounce bottle of the same juice normally costs $4.50 and is on sale for 10% off. Which is the better buy?

Small bottle: $ 3.00 \times (1 - 0.25) = 3.00 \times 0.75 = 2.25 $ dollars, so the unit price is $ \dfrac{2.25}{12} \approx 0.19 $ dollars per ounce.

Large bottle: $ 4.50 \times (1 - 0.10) = 4.50 \times 0.90 = 4.05 $ dollars, so the unit price is $ \dfrac{4.05}{20} \approx 0.2025 $ dollars per ounce.

Even though the small bottle has the bigger discount, it still has the lower unit price. The 12-ounce bottle is the better buy.

Sale price and unit price for the two juice bottles after their discounts

Worked example 2: Comparing a coupon to a percent discount

A 5-pound bag of rice costs $8.00 and has a coupon that takes $2.00 off. A 3-pound bag of the same rice costs $5.40 and is on sale for 15% off. Which is the better buy?

Large bag: $ 8.00 - 2.00 = 6.00 $ dollars, so the unit price is $ \dfrac{6.00}{5} = 1.20 $ dollars per pound.

Small bag: $ 5.40 \times (1 - 0.15) = 5.40 \times 0.85 = 4.59 $ dollars, so the unit price is $ \dfrac{4.59}{3} = 1.53 $ dollars per pound.

The 5-pound bag with the dollar-off coupon is the better buy, since $ 1.20 $ dollars per pound is less than $ 1.53 $ dollars per pound.

Tips for comparing discounted prices

Always convert every discount into an actual dollar amount before comparing, never compare raw percent discounts to each other.
Make sure the units match (ounces to ounces, not ounces to a whole package) before you compare unit prices.
Round numbers first to estimate which item looks cheaper, then compute exact values to confirm your estimate.
Watch for extra conditions, like "buy one get one 50% off," which change the effective discount rate across multiple items.

These same comparison skills connect closely to reading and evaluating data claims, such as spotting a misleading price comparison in an ad; you can explore that idea further in critiquing data presentation.

Related lessons

Tx Grade 8