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Mixture Problems

Mixture problems involve combining two or more quantities with different concentrations or values to form a single mixture with a desired property (such as concentration, strength, or cost).

General Principle:

The total amount of a substance from all parts is equal to the amount of that substance in the resulting mixture.

$$ v_1c_1 + v_2c_2 = (v_1 + v_2)c_f $$

Where:

$v_1$, $v_2$ – volume or weight of each component
$c_1$, $c_2$ – concentration, strength, or unit value of each component
$c_f$ – final concentration or value of the resulting mixture

Alternate Form:

You may also express each part individually as:

$$ \text{Amount} = \text{Volume} \times \text{Concentration} $$

This principle applies whether you are working with salt in water, alcohol in liquid, or cost per kilogram in blended goods.

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