Percentage Changes

Background

Special-offer packs often illustrate the extra free quantity by shading similar to that on the packet of biscuits in the programme. How accurate, or misleading, is such packaging? (While making the programme, we found many examples of packaging on which the illustration represented more than was actually being given for free. The example in the programme showed an offer of 20% extra free, so the portion of the packet shaded to show this should be one-sixth of the packet, not one-fifth - but marketers appear to miss the point that the new packet is 120% of the original, not 100%! Students could usefully investigate the mathematics of such implicit marketing and draw their own conclusions.

Rounding both percentages and pack sizes is another fruitful area. Offers tend to be to the nearest 5% or 10%, pack sizes to the nearest 10, 50 or 100 units. Is rounding normally geared to the benefit of the consumer or the retailer? Offers involving a third off, for example, will generally be rounded. Students could investigate the approximations used and their implications.