In chemistry lab, Stephanie has to make a 37 milliliter...

In chemistry lab, Stephanie has to make a 37 milliliter solution that is $12 \%$ HCl. All that is in the lab is $8 \%$ and $15 \%$ HCl. How many milliliters of each solution should she use to obtain the desired mix?

Key Concepts

Mixture Problems

Mixture problems involve combining different substances or solutions, each with a distinct property (such as concentration), to achieve a final mixture with a desired overall property or concentration. This concept is fundamental in both chemistry and algebra, as it requires understanding how the properties of individual components contribute to the average or total in the mixture.

Concentration and Percentages

Concentration in a solution is often expressed as a percentage, which represents the ratio of the solute's amount to the total amount of solution. This concept is critical for determining the strength or potency of a solution, and is widely used in chemistry to describe how much of an active component is present.

Weighted Average

The weighted average is a method used to determine the overall concentration of a mixture by multiplying each individual concentration by its corresponding fraction of the total volume and then summing the results. This allows for the accurate calculation of the final concentration when mixing solutions with different strengths.

Systems of Equations

Systems of equations are often employed to solve mixture problems. One equation typically accounts for the total volume of the mixture, while another accounts for the total amount of the solute. Solving these equations simultaneously yields the precise amounts of each component needed to achieve the desired final mixture.

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