a soccer player gets 2 points for a goal and 1 point for an assist. if the combined number of goals and assists that a player has is 24, and the total number of points that the player has is 42, which system of equations can be used to determine the number of goals and assists the player has? assume $g$ represents the number of goals and $a$ represents the number of assists.

$\bigcirc$ $g + a = 24$
$g + 2a = 42$

$\bigcirc$ $g + a = 24$
$2g + a = 42$

$\bigcirc$ $g + a = 42$
$g + 2a = 24$

$\bigcirc$ $g + a = 42$
$2g + a = 24$

Question

a soccer player gets 2 points for a goal and 1 point for an assist. if the combined number of goals and assists that a player has is 24, and the total number of points that the player has is 42, which system of equations can be used to determine the number of goals and assists the player has? assume \$g\$ represents the number of goals and \$a\$ represents the number of assists.

\$\bigcirc\$ \$g + a = 24\$
\$g + 2a = 42\$

\$\bigcirc\$ \$g + a = 24\$
\$2g + a = 42\$

\$\bigcirc\$ \$g + a = 42\$
\$g + 2a = 24\$

\$\bigcirc\$ \$g + a = 42\$
\$2g + a = 24\$

$\bigcirc$ $g + a = 24$
$g + 2a = 42$

$\bigcirc$ $g + a = 24$
$2g + a = 42$

$\bigcirc$ $g + a = 42$
$g + 2a = 24$

$\bigcirc$ $g + a = 42$
$2g + a = 24$

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", "System of Equations Translation" ], "new_concepts": [], "current_concepts": [ "Variable Identification", "Algebraic Translation", "System of Equations Translation" ] } ## Identify the variables Using the *Variable Identification* knowledge point $$ \begin{aligned} g &= \text{number of goals} \ a &= \text{number of assists} \end{aligned} $$ ## Translate the quantity relationship Using the *Algebraic Translation* knowledge point $$ g + a = 24 $$ ## Translate the value relationship Using the *System of Equations Translation* knowledge point $$ 2g + 1a = 42 \implies 2g + a = 42 $$ ## Formulate the system of equations Using the *System of Equations* knowledge point $$ \begin{cases} g + a = 24 \ 2g + a = 42 \end{cases} $$

(A) $g + a = 24$ $g + 2a = 42$

(B) $g + a = 24$ $2g + a = 42$

(C) $g + a = 42$ $g + 2a = 24$

(D) $g + a = 42$ $2g + a = 24$

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

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QUESTION IMAGE

Question

Explanation:

Identify the variables

Translate the quantity relationship

Translate the value relationship

Formulate the system of equations

Answer: