Additional Math Pages & Resources

Monday, May 2, 2011

Grand Complications, Part I

In the world of mechanical watches, there's a term called Grand Complication. It means that the watch performs several difficult functions, such as chiming the time of day, showing the phase of the moon, and serving as a stopwatch. It has to be able to do all these things at once, proving that its maker was highly skilled in design and fabrication of tiny mechanisms.

Photo from SJX of the PuristS

Elementary mathematics (as taught in our Excel Math curriculum) may sometimes lead you into grand complication calculations. (the more common description is higher-order thinking skills). This kind of problem-solving requires us to analyze the situation, learn some new facts that we've never known before, and combine multiple techniques or skills.

Here's an example:

I'm having a pint of bitter in the UK. The glass seems larger than a pint glass in the USA. The price seems reasonable, but I'm not sure how it translate to the cost of a pint back home. How can I compare them? I want to know the equivalent cost per unit of beverage.

A fair amount of time elapsed before I solved this grandly-complicated issue. Here are the calculations:

UNITS OF VOLUME
A pint glass in the UK  and a pint glass in the USA - are they the same volume? Research tells me that a pint glass is:
  • 20 fluid ounces (570 mL) in the UK [ a UK ounce = 28.41 ml ]
  • 16 fluid ounces (473 mL) in the USA [ a US ounce =  29.57 ml ]
No, the glasses do not contain the same volume of liquid. The volume of the pints are different and the volume of the ounces are different. The best way to find an equivalent price is to compare equivalent volumes. Let's use a liter. We need a conversion factor we'll call V, so we can change each of the "pints" to a liter.
  • How many UK pints to a liter?  1000 ÷ 570 ml = V so V = 1.75
  • How many US pints to a liter?  1000 ÷ 473 ml = V so V = 2.11
CURRENCY
A pint glass cost £2.50 in the UK. How much is that in US dollars?
  • the exchange rate today is 1.67 US dollars to 1 pound sterling
  • therefore 1.67 x  £2.50 = $4.17 US dollars for a UK pint
A US pint glass of bitters in my local restaurant is $5.00 US

COST PER UNIT
 How much is the price, in US dollars, per liter of bitters?
  •  UK $4.17 x 1.75 = $7.30
  •  US $5.00 x 2.11 = $10.55
CONCLUSIONS
It's cheaper in England. This is a very complicated problem to solve, but only simple math computation skills were needed - I used multiplication, division, ratios, volume, price per unit and foreign exchange.

This is indeed a Grand Complication Math Problem.

In doing this research I noticed that my local place proudly offers bitters in a 20 oz. glass.

To which I reply, US or UK ounces?