clara has pennies and quarters in her purse. she counts a total of 28 coins. if the total value of the coins is 76 cents, which system of equations can be used to determine the number of pennies and the number of quarters? assume $p$ represents the number of pennies and $q$ represents the number of quarters.

$\bigcirc$ $p + q = 28$
$p + 25q = 76$

$\bigcirc$ $p + q = 28$
$25p + q = 76$

$\bigcirc$ $p + q = 76$
$p + 25q = 28$

$\bigcirc$ $p + q = 76$
$25p + q = 28$

Question

clara has pennies and quarters in her purse. she counts a total of 28 coins. if the total value of the coins is 76 cents, which system of equations can be used to determine the number of pennies and the number of quarters? assume $p$ represents the number of pennies and $q$ represents the number of quarters.

$\bigcirc$ $p + q = 28$
$p + 25q = 76$

$\bigcirc$ $p + q = 28$
$25p + q = 76$

$\bigcirc$ $p + q = 76$
$p + 25q = 28$

$\bigcirc$ $p + q = 76$
$25p + q = 28$

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", "System of Equations Translation" ], "new_concepts": [], "current_concepts": [ "Variable Identification", "System of Equations Translation", "System of Equations" ] } ## Identify the variables Using the *Variable Identification* knowledge point $$ \begin{aligned} p &= \text{number of pennies} \ q &= \text{number of quarters} \end{aligned} $$ ## Translate the total coin count Using the *System of Equations Translation* knowledge point $$ p + q = 28 $$ ## Translate the total value Using the *System of Equations Translation* knowledge point $$ \begin{aligned} \text{Value of } p \text{ pennies} &= 1p \text{ cents} \ \text{Value of } q \text{ quarters} &= 25q \text{ cents} \ p + 25q &= 76 \end{aligned} $$ ## Combine into a system Using the *System of Equations* knowledge point $$ \begin{cases} p + q = 28 \ p + 25q = 76 \end{cases} $$

(A) $p + q = 28$ $p + 25q = 76$

(B) $p + q = 28$ $25p + q = 76$

(C) $p + q = 76$ $p + 25q = 28$

(D) $p + q = 76$ $25p + q = 28$

{ "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 total coin count

Translate the total value

Combine into a system

Answer: