the ratios are inversely proportional. find the missing variable.

if $t_1 = 6$, $s_1 = 3$, and $s_2 = 2$, what is the value of $t_2$?

Question

the ratios are inversely proportional. find the missing variable.

if $t_1 = 6$, $s_1 = 3$, and $s_2 = 2$, what is the value of $t_2$?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Basic Arithmetic Operations", "Linear Equations Solving" ], "new_concepts": [ "Inverse Proportion Equations" ], "current_concepts": [ "Basic Arithmetic Operations", "Linear Equations Solving", "Inverse Proportion Equations" ] } ## Set up the inverse proportion equation $$ t_1 \cdot s_1 = t_2 \cdot s_2 $$ ## Substitute the given values $$ 6 \cdot 3 = t_2 \cdot 2 $$ ## Solve for the missing variable $$ \begin{aligned} 18 &= 2t_2 \ t_2 &= 9 \end{aligned} $$ $t_2 = 9$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Proportion Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the inverse proportion equation

Substitute the given values

Solve for the missing variable

Answer: