A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to obtain 100 milliliters of a mixture that is 7% silver nitrate. How many milliliters of each of the solutions must be used?

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Define variables for the volumes of the two solutions: let $x$ be the milliliters of the 34% silver nitrate solution, and $y$ be the milliliters of the 4% silver nitrate solution.

Write the equation representing the total volume of the mixture: $x + y = 100$.

Write the equation representing the total amount of silver nitrate in the mixture using the percentages: $0.34x + 0.04y = 0.07 \times 100$.

Use the first equation to express one variable in terms of the other, for example, $y = 100 - x$.

Substitute $y = 100 - x$ into the silver nitrate equation and solve for $x$, then use that value to find $y$.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mixture Problems

Mixture problems involve combining two or more solutions with different concentrations to achieve a desired concentration. The key is to set up equations based on the total volume and the amount of solute in each solution, ensuring the final mixture meets the specified concentration.

Setting Up Algebraic Equations

To solve mixture problems, define variables for unknown quantities and translate the problem's conditions into algebraic equations. This often involves expressing the total volume and the total amount of solute as sums of parts from each solution.

Percent Concentration

Percent concentration represents the amount of solute in a solution as a percentage of the total solution volume. Understanding how to convert percentages to decimals and use them in calculations is essential for determining the quantities of each solution in the mixture.

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