Set up and solve the required proportion. Caffeine Many...

Set up and solve the required proportion. Caffeine Many convenience stores sell supersize 44-ounce soft drinks in refillable cups. For each of the products listed in the table, find the amount of caffeine contained in one of the large cups. Round to the nearest milligram. $$\begin{array}{|c|c|}\hline \begin{array}{c}\text { Soft drink, } \\\mathbf{1 2} \mathbf{o z} \end{array} & \begin{array}{c}\text { Caffeine } \\\mathbf{( m g )}\end{array} \\\hline \text { Mountain Dew } & 55 \\\hline \text { Coca-Cola Classic } & 47 \\\hline \text { Pepsi } & 37 \\\hline\end{array}$$

Set up and solve the required proportion.
Caffeine Many convenience stores sell supersize 44-ounce soft drinks in refillable cups. For each of the products listed in the table, find the amount of caffeine contained in one of the large cups. Round to the nearest milligram. $$\begin{array}{|c|c|}\hline \begin{array}{c}\text { Soft drink, } \\\mathbf{1 2} \mathbf{o z}
\end{array} & \begin{array}{c}\text { Caffeine } \\\mathbf{( m g )}\end{array} \\\hline \text { Mountain Dew } & 55 \\\hline \text { Coca-Cola Classic } & 47 \\\hline \text { Pepsi } & 37 \\\hline\end{array}$$

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Key Concepts

Cross-multiplication Method

This is a technique used to solve equations where two ratios are set equal to each other. By cross-multiplying, you can move from a proportion of known quantities to compute the unknown variable. It’s a fundamental algebraic method for solving direct variation problems like this one.

Rounding

After calculating the precise value of the caffeine content for the 44-ounce serving, the result may be a decimal. Rounding is used to convert this decimal to the nearest whole number or specified unit—in this case, the nearest milligram—to provide a practical answer for everyday use.

Proportional Reasoning

This concept involves understanding that if two quantities are directly related, changing one will change the other in a consistent manner. In this context, it means that the amount of caffeine in a soft drink scales directly with the volume of the drink, allowing you to set up a ratio or proportion based on known quantities to solve for an unknown amount.

Unit Rate Calculation

Calculating the unit rate involves finding the amount of caffeine per one ounce of the beverage. Once you determine how much caffeine is present per ounce, you can directly scale this amount to the desired volume, such as 44 ounces. This step is essential in converting known values to different units efficiently.

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