lesson 7 exit ticket

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?

Question

lesson 7 exit ticket

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?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Equations", "Proportional Relationships" ], "new_concepts": [ "Ratio Word Problems", "Part-to-Whole Ratios" ], "current_concepts": [ "Proportional Relationships", "Linear Equations", "Ratio Word Problems", "Part-to-Whole Ratios" ] } ## Set up the ratio equation $$ \begin{aligned} &\text{Let } x \text{ be the common multiplier.}\ &\text{Seltzer} = 3x\ &\text{Fruit juice} = 4x\ &\text{Total punch} = 3x + 4x = 7x \end{aligned} $$ ## Solve for the multiplier $$ \begin{aligned} 7x &= 42\ x &= 6 \end{aligned} $$ ## Calculate the individual quantities $$ \begin{aligned} &\text{Seltzer} = 3(6) = 18 \text{ cups}\ &\text{Fruit juice} = 4(6) = 24 \text{ cups} \end{aligned} $$ Raquel will need 18 cups of seltzer and 24 cups of fruit juice. { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Algebra", "Ratio Word Problems" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the ratio equation

Solve for the multiplier

Calculate the individual quantities

Answer: