Problem of the Week

Sydney House Prices
In last Saturday’s newspaper, an article on Sydney house prices argued that they are falling from their peak. In this table you can see that house prices in the suburb of Cabramatta have fallen by 2.27%: from a peak price of $1.1 million to a price of $1.1 million. How is this possible?

Petrol Price Comparison
To compare petrol prices (cost/volume) across countries, you need to know the exchange rate for the currency (we use AUD) and use the same unit of volume (we use litres). Last week, regular petrol in New Zealand was selling for 2.859 New Zealand dollars (NZD) per litre, while in the United States regular petrol was selling for 4.699 US dollars (USD) per gallon. Which was the less expensive? (Use these conversions: 1 gallon = 3.8 L, 1 USD = 1.37 AUD, 1 NZD = 0.93 AUD)

Peg Pattern
If there is 10cm between consecutive pegs within a group of 2 or 3 pegs, and there is 15cm between groups, how far is it between the first peg and the last peg pictured here? How did you work it out? If this pattern continues for 100 socks, what will be the distance between the first and last peg?