A person buys two plots to build a factory: one of 17,840 dam2 at 675 F per square metre, the other of 5,760 m2 at 6,850 F per square metre. Find the total price of the land, then the cost price once buildings costing 125,000,000 F are added.

Step-by-step solution

1. 1

   Convert the first plot to square metres. A decametre is $10$ m, so a square decametre is $10^2 = 100$ square metres — the conversion factor for an area is the square of the one for a length:

   $17{,}840\ \text{dam}^2 = 17{,}840 \times 100 = 1{,}784{,}000\ \text{m}^2$

   Using $10$ instead of $100$ here would understate the plot tenfold.

2. 2

   Price the first plot.

   $1{,}784{,}000 \times 675 = 1{,}204{,}200{,}000\ \text{F}$

   Breaking it up: $1{,}784{,}000 \times 600 = 1{,}070{,}400{,}000$ and $1{,}784{,}000 \times 75 = 133{,}800{,}000$; their sum is $1{,}204{,}200{,}000$.

3. 3

   Price the second plot. This one is already in square metres:

   $5{,}760 \times 6{,}850 = 39{,}456{,}000\ \text{F}$

4. 4

   Add for the total land price.

   $1{,}204{,}200{,}000 + 39{,}456{,}000 = 1{,}243{,}656{,}000\ \text{F}$

5. 5

   Add the construction cost for the cost price.

   $1{,}243{,}656{,}000 + 125{,}000{,}000 = 1{,}368{,}656{,}000\ \text{F}$

6. 6

   Check the order of magnitude. The first plot is $310$ times larger than the second but sold at roughly a tenth of the price per square metre, so it should dominate by a factor near $30$ — and indeed $\tfrac{1{,}204{,}200{,}000}{39{,}456{,}000} = 30.5$. A commonly circulated figure of $1{,}203{,}600{,}000$ F for the first plot is $600{,}000$ F short; dividing it by $675$ gives $1{,}783{,}111.1\ \text{m}^2$, not a whole number of square metres, which flags the error.