A recipe uses \(2~\text{cups}\) of rice for \(5~\text{servings}\). Evaluate every representation card against this proportional relationship.
Card A: A ratio table with pairs \((2,~5)\), \((4,~10)\), \((6,~15)\)
Card B: A ratio table with pairs \((2,~5)\), \((5,~12)\), \((8,~20)\)
Card C: A double number line where cups of rice are \(0,~2,~4,~6\) and servings are \(0,~5,~10,~15\)
Card D: A double number line where cups of rice are \(0,~2,~3,~4\) and servings are \(0,~5,~8,~10\)
Card E: The statement “\(10~\text{servings}\) need \(4~\text{cups}\) of rice.”
Card F: The statement “\(1~\text{serving}\) needs \(2.5~\text{cups}\) of rice.”
Report the complete set of cards that matches \(2~\text{cups}\) for \(5~\text{servings}\).
What this problem is really about
Every matching card must preserve rice first, servings second, and the two-to-five relationship in every displayed pair. We’ll test all rows of both tables, all aligned ticks on both number lines, and both verbal statements using common scale factors or cross products. We’ll also distinguish cups per serving from its reciprocal before reporting the complete set.