two rules for creating a pattern are given below.

rule 1: divide $x$ by 4 to get $y$.

rule 2: subtract 18 from $x$ to get $y$.

which ordered pair, $(x, y)$, works for both rules?

choose 1 answer:

a $(24, 6)$

b $(30, 12)$

c $(32, 8)$

Question

two rules for creating a pattern are given below.

rule 1: divide $x$ by 4 to get $y$.

rule 2: subtract 18 from $x$ to get $y$.

which ordered pair, $(x, y)$, works for both rules?

choose 1 answer:

a $(24, 6)$

b $(30, 12)$

c $(32, 8)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Algebraic Rules" ], "new_concepts": [ "Systems of Equations" ], "current_concepts": [ "Algebraic Rules", "Function Tables", "Systems of Equations" ] } ## Translate rules into algebraic equations $$ \begin{aligned} &\text{Rule 1: } y = \frac{x}{4}\ &\text{Rule 2: } y = x - 18 \end{aligned} $$ ## Test the given options $$ \begin{aligned} &\text{Option A: } (24, 6) \implies x = 24, y = 6\ &\text{Rule 1: } 6 = \frac{24}{4} \implies 6 = 6 \quad (\text{True})\ &\text{Rule 2: } 6 = 24 - 18 \implies 6 = 6 \quad (\text{True}) \end{aligned} $$ ## Verify other options for completeness $$ \begin{aligned} &\text{Option B: } (30, 12) \implies x = 30, y = 12\ &\text{Rule 1: } 12 = \frac{30}{4} \implies 12 = 7.5 \quad (\text{False})\ &\text{Option C: } (32, 8) \implies x = 32, y = 8\ &\text{Rule 2: } 8 = 32 - 18 \implies 8 = 14 \quad (\text{False}) \end{aligned} $$

(A) (24, 6)

(B) (30, 12)

(C) (32, 8)

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Translate rules into algebraic equations

Test the given options

Verify other options for completeness

Answer: