the maximum number of grams of fat (f) that should be in a diet varies directly as a persons weight (w). a person weighing 120 lb should have no more than 80 g of fat per day. what is the maximum daily fat intake for a person weighing 72 lb?

the maximum daily fat intake is g.

Question

the maximum number of grams of fat (f) that should be in a diet varies directly as a persons weight (w). a person weighing 120 lb should have no more than 80 g of fat per day. what is the maximum daily fat intake for a person weighing 72 lb?

the maximum daily fat intake is g.

the maximum daily fat intake is   g.

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": [ "Direct Variation", "Constant of Variation" ], "new_concepts": [], "current_concepts": [ "Direct Variation", "Constant of Variation" ] } ## Set up the direct variation equation Using the **Direct Variation** knowledge point $$ F = k \cdot W $$ ## Find the constant of variation Using the **Constant of Variation** knowledge point $$ \begin{aligned} 80 &= k \cdot 120 \ k &= \frac{80}{120} = \frac{2}{3} \end{aligned} $$ ## Calculate the fat intake for a 72 lb person Using the **Direct Variation** knowledge point $$ \begin{aligned} F &= \frac{2}{3} \cdot 72 \ F &= 2 \cdot 24 = 48 \end{aligned} $$ The maximum daily fat intake is 48 g. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Direct Variation" ] }

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Question

Explanation:

Set up the direct variation equation

Find the constant of variation

Calculate the fat intake for a 72 lb person

Answer: