# How many liters of a 7% solution of salt should be added to a 27% solution in order to obtain 640 liters of a 12% solution?

##### 2 Answers

#### Explanation:

Let the volume of 7% solution be

Let the volume of 27% solution be

Let the target volume of 12% solution be

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In this situation we have two separate condition that link the proportions.

Relationship by total volume:

By % content:

Two unknowns and two equations. Thus solvable.

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Consider

Multiply both sides by 100

Divide both sides by 20

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Substitute into

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Alternative and more efficient approach.

#### Explanation:

Let the volume of 7% solution be

Let the volume of 27% solution be

Let the target volume of 12% solution be

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Thus we have by percentage we have:

By substitution for

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Thus