# A chief wishes to make a dish that requires a blend of white and brown sugar?

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The recipe quantities in the book are to great for the number of people he is preparing the dish for. The proportions in the book are: #3/4# cup of white sugar and #1/2# cup of brown. The chief wishes to change the quantities such that he only uses #1/6# cup of brown. What proportion of a cup of whit sugar should he use.

The recipe quantities in the book are to great for the number of people he is preparing the dish for. The proportions in the book are:

##### 1 Answer

#### Explanation:

Assumption: The other sugar at

Let the unknown proportion of white sugar be

A fractions structure is

So we need to change the 'size indicators' such that they are all the same. That way we may directly compare just the 'counts'.

initial white sugar

initial brown sugar

target brown sugar

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Initial condition of

Writing this ratio in fraction form gives:

But we need:

Multiply both sides by 2 giving:

So measuring in cups we have

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Thus the ratio of the reduced volumes is:

Changing this to the same order as in the question: