Best Buys

The same thing is often sold in different sizes, or with different offers. The best buy, or the best value for money, is the option that gives you the most for your money. The biggest pack is not always the best value.

To decide, work out one value for every option that can be compared fairly: the price of one item, the price of the same amount of each (such as 100 g or 1 litre), or how much you get for each £1.

In the exam you are usually asked "Which is the better value for money?", for 2 to 4 marks, on calculator and non-calculator papers. Other questions ask you to work out a price per 100 g, or how much cheaper one option is than another.

The comparison must be shown. Write down the value you worked out for every option, with its units, and then a sentence saying which is better value. Naming the right option with no values gets no marks.

The price per unit is the cost of one item, or of one gram, 100 g or one litre. Work it out by dividing the cost by the amount.

\text{price per unit} = \text{cost} \div \text{amount}

For example, 5 pens for £3 cost \pounds 3 \div 5 = \pounds 0.60, which is 60p per pen. Divide the cost by the amount, not the amount by the cost.

The lower price per unit is the better value. Give every price per unit in the same unit, all in pence or all in pounds, so that they are easy to compare.

When packs hold different amounts, find the price of the same amount from each, such as the price per 100 g, per kilogram or per litre. Use the same amount for every option.

First write both amounts in the same unit, using these facts.

1 \text{ kg} = 1000 \text{ g} \qquad 1 \text{ litre} = 1000 \text{ ml}

To find the price per 100 g, work out how many lots of 100 g are in the pack, then divide the price by that number. A 500 g pack is 5 lots of 100 g, so if it costs £1.75 the price per 100 g is 175 \div 5 = 35p.

The cost of the same amount. Work out what the same amount costs with each pack. Choose an amount that every pack size goes into. For boxes of 4 eggs and boxes of 6 eggs, compare the cost of 12 eggs: 3 boxes of 4 or 2 boxes of 6.

The amount for each £1. Divide the amount by the cost. A 600 g bag of pasta for £1.50 gives 600 \div 1.5 = 400 g for each £1.

Be careful which way round the answer goes. With a price per unit or the cost of the same amount, the lower number is better value. With an amount for each £1, the higher number is better value, because you get more for each pound.

Any of these methods is fine, as long as you use the same one for every option and then say which is better value.

An offer changes what you pay or how much you get. Before comparing, write down how many you get and what you pay with each offer.

• 3 for the price of 2: you get 3 items and pay for 2.
• Buy one, get one half price: 2 items cost the full price plus half the price.
• 20\% off: the price goes down by 20\%, and the amount stays the same.
• 25\% extra: you get 25\% more for the same price.

For example, mugs cost £6 each with the offer "3 for the price of 2". Then 3 mugs cost 2 \times \pounds 6 = \pounds 12, which is \pounds 12 \div 3 = \pounds 4 per mug.

An offer only works on complete groups. With "3 for the price of 2", 7 items are two groups of 3, where you pay for 4, plus 1 more at full price. So you pay for 5 items. Packs work the same way: you can't buy part of a pack, so 14 rolls in packs of 4 means buying 4 packs, which is 16 rolls.

Some questions compare prices in two countries, such as the UK and Spain. The prices are in different currencies, so change one of them first, to make both prices the same currency.

The exchange rate tells you how. If £1 = 1.20 euros, multiply by 1.20 to change pounds into euros, and divide by 1.20 to change euros into pounds.

Check that your answer makes sense: here the amount in euros is always a bigger number than the same amount in pounds. Then make the amounts match, as before, and keep all the figures on your calculator until the end.

• Dividing the wrong way round. Divide the cost by the amount, so 12 items for £6 cost 6 \div 12 = \pounds 0.50 each.
• Mixing pounds and pence. Give every value in the same unit: £0.45 is 45p, not 0.45p.
• Comparing amounts that don't match. Doubling a pack of 8 gives 16, not 12, so find the price per item or the cost of the same number from each.
• Using an offer wrongly. Write down how many you get and what you pay with each offer before you compare.
• Choosing the smaller amount for each £1. With an amount for each £1, the bigger number is better value.
• Giving a decision with no values. Write the value for every option, then say which is better value.