Question

The ratio of butter:flour:sugar in a recipe is 1:9:6. When using 8 cups of sugar in this recipe, how many total cups of ingredients will be used? Express your answer as a common fraction.

Answer 1

to find that out, let's divide 8 by (1+9+6) and distribute accordingly.

$\bf \begin{array}{cccccc} \stackrel{butter}{1\left( \frac{8}{1+9+6} \right)}&:&\stackrel{flour}{9\left( \frac{8}{1+9+6} \right)}&:&\stackrel{sugar}{6\left( \frac{8}{1+9+6} \right)}\\\\\\ 1\left( \frac{1}{2} \right)&:&9\left( \frac{1}{2} \right)&:&6\left( \frac{1}{2} \right) \\\\\\ \cfrac{1}{2}&:&\cfrac{9}{2}&:&\cfrac{6}{2}\implies \cfrac{3}{1} \end{array}$