Trail mix has \(\text{nuts}:\text{dried}~\text{fruit}~=~5:8\) and must scale to \(20~\text{cups}\) of nuts. Consider these strategies: A, find a multiplicative scale factor; B, add the change to \(\text{both}~\text{terms}\); C, scale only nuts; D, use a factor of \(5\). Choose the strategy that works, then complete the ratio.

A valid strategy must connect five cups of nuts to the twenty-cup target and preserve the nuts-to-dried-fruit relationship. We’ll carry out each proposed method far enough to see whether both terms remain linked by the same proportional change and whether the nuts amount reaches the target. Scaling the resulting pair back to the original will verify whether the method preserves the recipe.