the local theater sells tickets to its plays at a rate of \$38 each. patrons who attend multiple shows are encouraged to buy an annual membership for \$80. members are able to buy tickets at a discounted rate of \$20 each. roger expects to attend 6 shows this year. grace expects to attend 4 shows. who would benefit from buying a membership this year?

neither grace nor roger
only grace
only roger
both grace and roger

Question

the local theater sells tickets to its plays at a rate of \\$38 each. patrons who attend multiple shows are encouraged to buy an annual membership for \\$80. members are able to buy tickets at a discounted rate of \\$20 each. roger expects to attend 6 shows this year. grace expects to attend 4 shows. who would benefit from buying a membership this year?

neither grace nor roger
only grace
only roger
both grace and roger

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Cost Comparison", "Linear Cost Models" ], "current_concepts": [ "Cost Comparison", "Linear Cost Models" ] } ## Calculate costs for Roger $$ \begin{aligned} &\text{Without membership (6 shows): } 6 \times \$38 = \$228 \ &\text{With membership (6 shows): } \$80 + (6 \times \$20) = \$80 + \$120 = \$200 \ &\$200 < \$228 \quad (\text{Roger benefits}) \end{aligned} $$ ## Calculate costs for Grace $$ \begin{aligned} &\text{Without membership (4 shows): } 4 \times \$38 = \$152 \ &\text{With membership (4 shows): } \$80 + (4 \times \$20) = \$80 + \$80 = \$160 \ &\$160 > \$152 \quad (\text{Grace does not benefit}) \end{aligned} $$ ## Determine the correct option $$ \text{Only Roger would benefit from buying a membership.} $$

neither Grace nor Roger

only Grace

only Roger

both Grace and Roger

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Cost Models" ] }

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Question

Explanation:

Calculate costs for Roger

Calculate costs for Grace

Determine the correct option

Answer: