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$\begin{tabular}{|l|c|c|} \hline \multicolumn{3}{|c|}{Energy per Gram of Typical Macronutrients} \\ \hline Macronutrient & Food calories & Kiljoules \\ \hline Protein & 4.0 & 16.7 \\ \hline Fat & 9.0 & 37.7 \\ \hline Carbohydrate & 4.0 & 16.7 \\ \hline \end{tabular}$ The table above gives the typical amounts of energy per gram, expressed in both food calories and kiljoules, of the three macronutrients in food. If the 180 food calories in a granola bar come entirely from $p$ grams of protein, $f$ grams of fat, and $c$ grams of carbohydrate, which of the following expresses $f$ in terms of $p$ and $c$ ?<br/><br/>\[\begin{array}{l}{\mbox{\small A}.}\ f=20+\frac{4}{9}(p+c)\\ \\ {\mbox{\small B}.}\ f=20-\frac{4}{9}(p+c)\\ \\ {\mbox{\small C}.}\ f=20-\frac{4}{9}(p-c)\\ \\ {\mbox{\small D}.}\ f=20+\frac{9}{4}(p+c)\\ \end{array}\]