Question

An artisanal baker is preparing a large batch of special dough. The recipe requires several ingredients, but they have to use up existing stock. They used 1/2 a cup of flour for a test batch, and then a large bin that held 3/4 of the total required amount. After adding both, they still need exactly 4 1/3 cups more flour to reach the total amount needed for the large batch. What is the total amount of flour required for the large batch?

Answer 1

Let the total required amount be T cups. They used 1/2 cup plus a bin holding (3/4)T, and still needed 4 1/3 cups:

T - (1/2 + (3/4)T) = 4 1/3
(1/4)T = 4 1/3 + 1/2 = 13/3 + 1/2 = 29/6
T = 4 * 29/6 = 116/6 = 58/3 = 19 1/3

So the large batch requires 19 1/3 cups of flour.