## FANDOM

44,133 Pages

8 November 2013
Logs 19 December 2007 34 28 Unchanged
Achey tree logs 40 39
Oak logs 18 12
Willow logs 22 20
Teak logs 136 71
Maple logs 46 30
Mahogany logs 173 392
Arctic pine logs 855 57
Yew logs 413 526
Magic logs 1,221 1,646

Calculations

From the old divisor obtained from the templates:

${div}_{\text{old}} = 10.0000$

We need to calculate a new divisor:

${div}_{\text{new}} = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}}$

To calculate the new divisor, we need to find:

\begin{align} \sum \left ( \frac{p}{q} \right )_{\text{old}} & = \text{sum of ratios prior to change} \\ & = \frac{280}{34} + \frac{399}{40} + \frac{123}{18} + \dots + \frac{1,646}{1,221} \\ & = 32.08119681 \text{ (up to 8 d.p.)} \end{align}

And also:

\begin{align} \sum \left ( \frac{p}{q} \right )_{\text{new}} & = \text{sum of ratios prior to change} - \text{sum of removed ratios} + \text{sum of added ratios} \\ & = \sum \left ( \frac{p}{q} \right )_{\text{old}} - \text{sum of removed ratios} + \text{number of added items} \\ & = 32.08119681 - 0 + 1 \\ & = 33.08119681 \text{ (up to 8 d.p.)} \end{align}

Thus, the new divisor is:

\begin{align} {div}_{\text{new}} & = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}} \\ & = 10.0000 \times \frac{33.08119681}{32.08119681} \\ & = 10.3117 \text{ (4 d.p.)} \end{align}
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