TV appearance on BBC `Watchdog'
Not my usual research but on the principle that `maths is useful’ I agreed to compute something for consumer affairs progamme `Watchdog’. Click on the above photo to follow the link (for as long as they keep it live) to see me on national TV for all of, er, 15 seconds (figuratively); they actually shot all morning but most of it was squeezed out by breaking news in the rest of the programme.
The background was a sample basket of 5 food products where the manufacturer had cut the amount of product over the last 3 months but kept the packaging the same. It means that when you buy the product you may not realise that you are actually paying for extra air where you had been paying for product. They asked me to work out how much. Its a nice application of a little algebra but the bottom line was that if everyone in the UK had just these 5 products in their weekly shop (or other products in the same situation) for a year, they would have purchased 56 hot air balloons worth of extra air!
If you watch the clip you will see me doing the following calculation. Let M be the original net weight and <i>d</i> M the change over the three months. If V is the original net volume and <i>d</i> V the change in product volume then,
as the product is assumed unchanged
<i>d</i> V/V= <i>d</i> M/M=r
say. Manufacturers don’t tend to record net volume so we don’t know what V is but let V’ be the current product volume. Then
V’=V-<i>d</i> V=V(1-<i>d</i> V/V) = V(1-r).
We can invert this to obtain V and hence
<i>d</i> V=Vr=V’r/(1-r).
One just puts in the observed r from the reduction in weights and the current product volume V’ and we are done. <i>It’s not rocket science but it does show that a little algebra can actually be useful.</i>
<b>Thursday, 22 April 2010</b>