john has to fix at least 12 watches in 40 hours. digital watches (x) take him 2 hours to fix and analog watches (y) take him 6 hours to fix.

complete the inequalities below to represent this situation:

\x + y \ge ?\
\ x + y \le 40\

Question

john has to fix at least 12 watches in 40 hours. digital watches (x) take him 2 hours to fix and analog watches (y) take him 6 hours to fix.

complete the inequalities below to represent this situation:

\x + y \ge ?\
\ x +  y \le 40\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Inequalities" ], "new_concepts": [ "Systems of Linear Inequalities", "Linear Inequality Modeling" ], "current_concepts": [ "Solving Inequalities", "Systems of Linear Inequalities", "Linear Inequality Modeling" ] } ## Define variables and constraints Using the *Solving Inequalities* knowledge point $$ \begin{aligned} &x = \text{number of digital watches}\ &y = \text{number of analog watches} \end{aligned} $$ ## Model the watch quantity constraint Using the *Solving Inequalities* knowledge point $$ \begin{aligned} &\text{Total watches} \ge 12\ &x + y \ge 12 \end{aligned} $$ ## Model the time constraint Using the *Solving Inequalities* knowledge point $$ \begin{aligned} &\text{Time for digital watches} = 2x\ &\text{Time for analog watches} = 6y\ &\text{Total time} \le 40\ &2x + 6y \le 40 \end{aligned} $$ John has to fix at least 12 watches in 40 hours. Digital watches ($x$) take him 2 hours to fix and analog watches ($y$) take him 6 hours to fix. Complete the inequalities below to represent this situation: $x + y \ge$ 12 2$x +$ 6$y \le 40$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Systems of Linear Inequalities" ] }

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QUESTION IMAGE

Question

Explanation:

Define variables and constraints

Model the watch quantity constraint

Model the time constraint

Answer: