Fraction word problems got me down

Question

A recipe calls for 3/4 cup of sugar and 2/3 cup of butter. I accidently used 1 and 1/2 cups of butter. How much sugar should I use?

Answer 1

A recipe calls for 3/4 cup of sugar and 2/3 cup of butter, so the sugar to butter ratio is

(3/4)/(2/3) = (3/4)(3/2) = 9/8.  This ratio implies that 1 cup of butter requires 9/8 cups of sugar.

 

Since you use 1½ = 3/2 cups of butter, you will need

(3/2)(9/8) = 27/16 cups of sugar.