Question

if the ratio of red objects to blue objects is 3:1 then what percent of the objects are red?

Answer 1

in plain and short, we simply divide the "whole" by the sum of the ratios, and distribute accordingly.

now, 100% is the whole of any amount, so we'll divide 100% by (3+1).

$\bf \cfrac{\textit{red objects}}{\textit{blue objects}}\qquad 3:1\qquad \cfrac{3}{1}\qquad \cfrac{3\cdot \frac{100}{3+1}}{1\cdot \frac{100}{3+1}}\implies \cfrac{3\cdot 25}{1\cdot 25}\implies \cfrac{75}{25}\implies \cfrac{75\%}{25\%}$