In this image, how much profit is the money changing business making?

anonymous

For the benefit of others, let me explain the way to read the table. I assume this table is for how much the money exchanger is selling and buying foreign currencies relative to the Great British Pound (£), since that currency isn't listed. Let's look at the US dollar (\$) numbers, for example. It is saying they will sell you £1 for \$1.5085 and will sell you \$1.2658 for £1 .

Assuming they make the same profit either way, the expected return, for lack of a better term, is the square root of the ratio of the smaller number to the larger number. In this case sqrt(1.2658/1.5085) = 91.60%. The difference from 100% is the money changer's profit, or the "house edge" to using a gambling term, which in this example is 8.40%.

### Currency Exchange Expected Return and House Edge

Return
House
Edge
Euro 1.1800 0.9959 91.87% 8.13%
USA 1.5085 1.2658 91.60% 8.40%
South Africa 15.7723 12.3244 88.40% 11.60%
Hong Kong 11.6445 9.8024 91.75% 8.25%
Japan 134.6200 108.9200 89.95% 10.05%
Australia 2.3282 1.8738 89.71% 10.29%
Switzerland 1.8179 1.4372 88.91% 11.09%
UAE 5.5920 4.4792 89.50% 10.50%
Saudi Arabia 5.8807 4.5588 88.05% 11.95%

There is a straight water pipe (blue) in the vicinity of points A and B. Point A is 2 miles from the closest point on the pipe. Point B is 3 miles from the closest point on the pipe. The two points along the pipe that mark the closest points to A and B are 5 miles apart. It is desired to lay two new pipes (red), linking A and B to the water-bearing pipe, having only one point of contact with the water pipe with the two new pipes going directly to A and B. In other words, the new pipes must form a V shape. What is the least distance of pipe required?

anonymous

5√2 =~ 7.071068 miles

Here is my solution (PDF)

There is a straight water pipe (blue) in the vicinity of points A and B. Point A is 2 miles from the closest point on the pipe. Point B is 3 miles from the closest point on the pipe. These two points along the pipe that mark the closest points to A and B are 5 miles apart. It is desired to provide water to points A and B by laying new pipes linking points A and B to anywhere along the blue pipe. These new pipes may be in any form you wish. What is the least distance of new pipe needed?

anonymous

The new pipes should form a Y shape, with one end leading to the existing water pipe and the other two ends leading to the two houses.

The point in (or in some cases out) of a triangle that minimizes the sum of the distances to each vertex is called the Fermat Point. I won't get into how to find it, but a property is that the lines it makes to the three vertexes form three 120° angles.