ACT-Style: Ratio and Proportion Word Problems

ACT Math · Axiom Academy

EXAMPLE ACT-Style: Ratio and Proportion Word Problems Scaling a recipe up — setting up a direct proportion correctly is the whole battle A recipe that makes 6 servings calls for 9 cups of vegetable broth . At this same rate, how many cups of broth are needed to make 18 servings ? Nice work — you set up and solved a direct proportion, which is the single most common ratio/proportion word-problem shape on the ACT. Same units, same position: — broth stays on top on BOTH sides, servings stays on the bottom on both sides. Flipping one side upside down (choice A, ) is the single most common ACT proportion trap. Scale by the NEW TOTAL, not the increase: the problem asks for the broth needed for all 18 servings, not just the extra 12 servings beyond the original 6 — scaling by the increase alone gives choice C ( ), a real number that answers a different question. Keep the right quantity in the right slot: swapping broth and servings in the proportion (choice B, ) silently solves for a "servings per cup" quantity instead of the cups of broth actually asked for. Proportional reasoning isn't additive: "6 more servings should need 6 more cups" (choice D, 9+12=21 ) ignores that broth scales at 1.5 cups per serving, not 1 cup per serving — additive reasoning only works when the rate happens to equal 1.

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