Best Buys

The Unit Price Method

• Step 1: Identify Units: Ensure you know the total cost and the total quantity for each option.
• Step 2: Standardize Units: Convert all quantities to the same unit (e.g., convert all weights to grams or all volumes to milliliters) to ensure a fair comparison.
• Step 3: Calculate: Divide the total price by the total quantity to find the cost per single unit.

Formula: $\text{Unit Price} = \frac{\text{Total Cost}}{\text{Total Quantity}}$

• Step 4: Compare: The option with the lowest numerical result from Step 3 is the 'Best Buy'.

The Common Quantity Method

• Instead of finding the price of 1 unit, find the price of a common multiple (e.g., if comparing 200g and 500g, find the price of 1000g for both).
• This method is often easier for mental math when the quantities share simple common multiples.

• Price per Unit vs. Unit per Price: While 'Price per Unit' ($Price \div Quantity$) tells you how much 1 unit costs, 'Unit per Price' ($Quantity \div Price$) tells you how much product you get for 1 dollar. Both can determine value, but the 'Best Buy' is the lowest for the former and the highest for the latter.

• Bulk vs. Individual: Larger packs are often assumed to be cheaper per unit, but marketing 'multi-buys' can sometimes be more expensive than buying individual items if not calculated carefully.

• Check the Units: Examiners often provide one quantity in grams and another in kilograms. Always convert to the smaller unit to avoid working with messy decimals early in the calculation.

• Rounding Precision: Do not round your unit price too early. If two items are very close in value, rounding to 2 decimal places might make them look identical when they are actually different.

• Multi-buy Offers: For 'Buy One Get One Free' or '3 for the price of 2' deals, calculate the total quantity received and divide the total price paid by that new quantity.

• Sanity Check: If a 1kg box costs 10 USD and a 500g box costs 4 USD, the 1kg box should be the better deal. If your math says otherwise, check if you divided in the wrong order.

• Division Order: A common mistake is dividing quantity by price ($Quantity \div Price$) but then looking for the lowest number. If you divide quantity by price, the largest number is the best value.

• Ignoring 'Hidden' Units: In some problems, items are sold in 'packs' of different sizes (e.g., a pack of 6 vs a pack of 10). Ensure you calculate the price per individual item rather than just comparing the pack prices.

• Currency Conversion: In advanced problems involving different currencies, you must convert to a single currency before calculating the unit price.