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Mathematics > Standard Multiple Choice

To make an orange dye, parts of red dye are mixed with parts of yellow dye. To make a green dye, parts of blue dye are mixed with part of yellow dye. If equal amounts of green and orange are mixed, what fraction of the new mixture is yellow dye?

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### Explanation

Suppose that quarts of the final mixture of dye will be made. Since it is to be made from equal amounts of orange and green dye, it will consist of quarts of orange dye and quarts of green dye. Since the orange dye has parts yellow dye for each parts total dye, of it is yellow dye. Similarly, of the green dye is yellow dye. The amount of yellow in the final mixture is given by

So of the final mixture is yellow dye.

Note: Although “quarts” were used to express the amount of the final mixture, it could have been pints or any other unit of liquid measure.

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