Which pack is the better buy?
Tonight's idea
Shops sell the same thing in packs of different sizes. A bigger pack costs more, but you get more. So the price on the shelf does not tell you which pack is the better deal.
The fair test is to find the price of one. Share the price of the pack equally among the things in it. This is called the unit price. "Unit" means one.
Price of one = price of the pack ÷ how many are in it. The lower price of one is the better buy.
It helps to work in cents. $2.70 is 270 cents, and \(270 \div 6 = 45\).
The same test works for weight. Find the price of 100 g, or of 1 kg, for each pack. One warning: a better buy only saves money if you use all of it.
Watch one: six rolls for $4 or ten for $6?
Ten for $6: \(600 \div 10 = 60\) cents each.
Six for $4: \(400 \div 6\) is 66 remainder 4, so nearly 67 cents each. The pack of ten is the better buy.
Check it another way. Buy the same number from each: 30 rolls.
\[5 \text{ packs of six} = 5 \times \$4 = \$20, \qquad 3 \text{ packs of ten} = 3 \times \$6 = \$18.\]Thirty rolls cost $2 less in packs of ten.
Your turn
- Find the price of one. (a) 5 apples for $2.00. (b) 8 pens for $3.20. (c) 12 eggs for $4.20.
- Which is the better buy? Show the price of one each time. (a) 3 bars for $1.80 or 5 bars for $2.75. (b) 4 cans for $3.00 or 6 cans for $4.80.
- Rice comes in a 500 g bag for $2.00 and a 2 kg bag for $7.00. Remember that 1 kg is 1000 g. (a) How many 500 g bags hold as much as one 2 kg bag? (b) Which is the better buy? (c) How much do you save by buying 2 kg the cheaper way?
- A pack of 10 pencils costs $6.00. (a) What should a pack of 6 cost to be exactly as good a buy? (b) The shop sells the pack of 6 for $3.50. Which pack is the better buy now? Say how you know without dividing by 6.
Stretch: at least eighteen
Rolls cost $4 for six or $6 for ten. You need at least 18 rolls. Find the cheapest way to buy them. Two different ways cost the same. Which would you pick, and why?
Answers
- (a) \(200 \div 5 = 40\) cents. (b) \(320 \div 8 = 40\) cents. (c) \(420 \div 12 = 35\) cents.
- (a) \(180 \div 3 = 60\) cents and \(275 \div 5 = 55\) cents. The pack of 5 is better. (b) \(300 \div 4 = 75\) cents and \(480 \div 6 = 80\) cents. The pack of 4 is better. The bigger pack is not always the cheaper one.
- (a) 2 kg is 2000 g, and \(2000 \div 500 = 4\) bags. (b) Four small bags cost \(4 \times \$2 = \$8\). The 2 kg bag costs $7, so it is the better buy. (c) \(\$8 - \$7 = \$1\).
- (a) One pencil costs \(600 \div 10 = 60\) cents. Six at that price cost \(6 \times 60 = 360\) cents, which is $3.60. (b) The pack of 6. It costs $3.50, which is less than $3.60, so each pencil in it must cost less than 60 cents.
Stretch. Three packs of six give exactly 18 rolls for \(3 \times \$4 = \$12\). Two packs of ten give 20 rolls for \(2 \times \$6 = \$12\). Nothing cheaper reaches 18: one of each gives only 16 rolls. For the same $12, two packs of ten give you two extra rolls. Pick those, unless the extra two would go to waste.