You have two brands of dietary supplements on your shelf....

You have two brands of dietary supplements on your shelf. Among other ingredients, both contain protein and carbohydrates. The amounts of protein and carbohydrates in one unit of each supplement are given in the following table as percentages of the recommended daily amount (RDA). How many units of each supplement do you need in a day to obtain the RDA for both protein and carbohydrates? $$\begin{array}{lcc} & \begin{array}{c} \text { Protein } \\ \text { (\% of RDA } \\ \text { in one unit) } \end{array} & \begin{array}{c} \text { Carbohydrates } \\ \text { (\% of RDA } \\ \text { in one unit) } \end{array} \\ \hline \text { Supplement #1 } & 8 & 12 \\ \text { Supplement #2 } & 16 & 4 \\ \hline \end{array}$$

You have two brands of dietary supplements on your shelf. Among other ingredients, both contain protein and carbohydrates. The amounts of protein and carbohydrates in one unit of each supplement are given in the following table as percentages of the recommended daily amount (RDA). How many units of each supplement do you need in a day to obtain the RDA for both protein and carbohydrates?
$$\begin{array}{lcc}
& \begin{array}{c}
\text { Protein } \\
\text { (\% of RDA } \\
\text { in one unit) }
\end{array} & \begin{array}{c}
\text { Carbohydrates } \\
\text { (\% of RDA } \\
\text { in one unit) }
\end{array} \\
\hline \text { Supplement #1 } & 8 & 12 \\
\text { Supplement #2 } & 16 & 4 \\
\hline
\end{array}$$

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Key Concepts

System of Linear Equations

This concept involves creating and solving multiple linear equations that share common variables. In problems where different components contribute to a total target (such as nutritional values), each component’s contribution can be represented as part of a linear equation. Solving the system identifies the exact amounts of each component required to meet all target conditions simultaneously.

Mixture Problems

Mixture problems focus on combining two or more substances, each with their own distinct properties, to achieve a desired overall composition. This approach is used to balance contributions from different sources and is widely applicable in contexts like chemistry, economics, and nutrition, where different mix ratios influence the final outcome.

Percentages and Proportions

Understanding percentages is essential for interpreting parts of a whole and establishing proportional relationships. When components are described in terms of percentages of a required total, these values can be used to set up equations that reflect how much each component contributes to reaching a complete target.

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