malia did push-ups and pull-ups in her physical education class. she did 24 push-ups and pull-ups combined, with each push-up taking her 2 seconds and each pull-up taking her 4 seconds. if she spent a total of 68 seconds doing the push-ups and pull-ups, how many pull-ups did she do?

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Question

malia did push-ups and pull-ups in her physical education class. she did 24 push-ups and pull-ups combined, with each push-up taking her 2 seconds and each pull-up taking her 4 seconds. if she spent a total of 68 seconds doing the push-ups and pull-ups, how many pull-ups did she do?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Variable Identification", "Algebraic Translation", "Substitution Method" ], "new_concepts": [], "current_concepts": [ "Variable Identification", "Algebraic Translation", "Substitution Method", "System of Equations" ] } ## Define the variables Using the *Variable Identification* knowledge point $$ \begin{aligned} x &= \text{number of push-ups Malia did} \ y &= \text{number of pull-ups Malia did} \end{aligned} $$ ## Translate the word problem into equations Using the *Algebraic Translation* knowledge point $$ \begin{aligned} x + y &= 24 \ 2x + 4y &= 68 \end{aligned} $$ ## Solve the system of equations Using the *Substitution Method* knowledge point $$ \begin{aligned} x &= 24 - y \ 2(24 - y) + 4y &= 68 \ 48 - 2y + 4y &= 68 \ 48 + 2y &= 68 \ 2y &= 20 \ y &= 10 \end{aligned} $$

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{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "System of Equations" ] }

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Explanation:

Define the variables

Translate the word problem into equations

Solve the system of equations

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