the ratio of seltzer to fruit juice in raquels punch recipe is 3:4. how much seltzer and how much fruit juice will raquel need to make 42 cups of punch?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Proportional Relationships" ], "new_concepts": [], "current_concepts": [ "Proportional Relationships", "Ratios" ] } ## Identify the given ratio and total quantity The ratio of seltzer to fruit juice is $3:4$. The total volume of punch required is $42$ cups. ## Calculate the total parts in the ratio $$ 3 + 4 = 7 \text{ parts} $$ ## Determine the volume of seltzer and fruit juice $$ \begin{aligned} \text{Seltzer} &= \frac{3}{7} \times 42 = 18 \text{ cups} \ \text{Fruit juice} &= \frac{4}{7} \times 42 = 24 \text{ cups} \end{aligned} $$ Raquel will need 18 cups of seltzer and 24 cups of fruit juice. { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Algebra", "Proportional Relationships" ] }

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Explanation:

Identify the given ratio and total quantity

Calculate the total parts in the ratio

Determine the volume of seltzer and fruit juice

Answer: