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

Total cups of ingredients:

Let the number of cups of flour to be added be $x$

Let the number of cups of butter to be added be $y$

Cups of sugar$=8$

Since the ratio of butter:flour:sugar in a recipe is $1:9:6$

$$\begin{gathered} \frac{x}{cupsofsugar}=\frac{9}{6} \\ \frac{x}{8}=\frac{9}{6} \\ \Rightarrow x=12 \end{gathered}$$

Hence we need $12$ cups of flour

Ratio of butter: flour is $1:9$

So

$$\begin{gathered} \frac{y}{12}=\frac{1}{9} \\ \Rightarrow y=\frac{4}{3} \end{gathered}$$

Hence we need $\frac{4}{3}$cups butter

Hence, Total number of cups of in gradients$=8+12+\frac{4}{3}=\frac{64}{3}$ cups