Question

Travis was attempting to make muffins to take to a neighbor. The recipe that he was using required 3/4 cup of sugar and 1/8 cup of butter. Travis accidentally put a whole cup of butter in the mix.
A.What is the ratio of the sugar to butter in the original recipe?

B.What amount of sugar does Travis need to mix to have the same ratio of sugar to butter that the original recipe calls for?

C.if Travis wants to keep the ratios the same as they are in the original recipe, how will the amounts of all the other ingredients for this new mixture compare to the amounts given in the recipe?

Answer 1

A. The recipe  required 3/4 cup of sugar and 1/8 cup of butter.

The ratio of the sugar to butter in the original recipe is

$\dfrac{\frac{3}{4}}{\frac{1}{8}}=\dfrac{3}{4}\cdot \dfrac{8}{1}=\dfrac{6}{1}.$

B. If Travis accidentally put a whole cup of butter in the mix, then he needs to put

$\dfrac{3}{4}\cdot \dfrac{6}{1}=\dfrac{9}{2}=4\dfrac{1}{2}$ cup of sugar.

C. Travis has to put 1/8 cup of butter, but he put 1 cup of butter. The ratio is

$\dfrac{1}{\frac{1}{8}}=\dfrac{1}{1}\cdot \dfrac{8}{1}=\dfrac{8}{1}.$

If Travis wants to keep the ratios the same as they are in the original recipe, he needs to put 8 times more of all the other ingredients.