mrs. roberts plants tomatoes and radishes in the areas shown in the model below.

tomatoes: 35 acres
radishes: 28 acres

which expression is equivalent to the sum of the two areas?

Question

mrs. roberts plants tomatoes and radishes in the areas shown in the model below.

tomatoes: 35 acres
radishes: 28 acres

which expression is equivalent to the sum of the two areas?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor", "Distributive Property", "Area Model", "Equivalent Expressions" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor", "Distributive Property", "Area Model", "Equivalent Expressions" ] } ## Identify the given areas Using the *Area Model* knowledge point $$ \begin{aligned} &\text{Tomatoes Area} = 35\text{ acres}\ &\text{Radishes Area} = 28\text{ acres}\ &\text{Total Area Sum} = 35 + 28 \end{aligned} $$ ## Find the Greatest Common Factor Using the *Greatest Common Factor* knowledge point $$ \begin{aligned} &\text{Factors of } 35: 1, 5, 7, 35\ &\text{Factors of } 28: 1, 2, 4, 7, 14, 28\ &\text{GCF}(35, 28) = 7 \end{aligned} $$ ## Apply the Distributive Property Using the *Distributive Property* and *Equivalent Expressions* knowledge points $$ \begin{aligned} &35 + 28 = 7 \times 5 + 7 \times 4\ &35 + 28 = 7(5 + 4) \end{aligned} $$ $7(5 + 4)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Equivalent Expressions" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given areas

Find the Greatest Common Factor

Apply the Distributive Property

Answer: