Proportionality calculations lead to the use of the so-called 'rule of 3', also nammed the 'cross product law'.
Let's study it with an example.
If it lasts 15 minutes to bake 500 g of rastbeef, how much time shalll I bake my 950 g rastbeef?
Let's call x the time in minutes that we are looking for.
Then the time per gram is either 15 min over 500 g, or x min over 950 g:
------ = ------ (1)
If we multiply both sides of (1) by the product 950 x 500 and simplify the left side by 500 and the right side by 950, we obtain the cross product law:
500 x = 950 x 15 (2)
where the numerator of a side is multiplied by the denominator of the other side.
(2) is a linear equation of the type a x = b, wich solution is x=a/b (a divided by b).
Thus the solution of our problem is the 'rule of 3' formula:
950 x 15
x = --------------- = 28.5 min = 28 min 30 s
The rule of 3 can be obtain directly from the proportionality equation (1), multiplying both sides of (1) by 950 and simplifying the left side by 950.
Thus, the rule of 3 solves a proportionality equation, that is in fact a linear equation as well, with coefficients inverses of integers…