iola has $75. she buys a pair of shoes on sale for one-half off and a pair of socks for $6. she has $32 left. which equation can be used to find x, the regular price of the shoes?

$x + 6 + 32 = 75$
$x + 6 = 32$
$\frac{1}{2}x + 6 + 32 = 75$
$\frac{1}{2}x + 32 = 75$

Question

iola has $75. she buys a pair of shoes on sale for one-half off and a pair of socks for $6. she has $32 left. which equation can be used to find x, the regular price of the shoes?

$x + 6 + 32 = 75$
$x + 6 = 32$
$\frac{1}{2}x + 6 + 32 = 75$
$\frac{1}{2}x + 32 = 75$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Algebraic Translation", "Linear Modeling" ], "new_concepts": [ "Linear Equation Formulation" ], "current_concepts": [ "Algebraic Translation", "Linear Modeling", "Linear Equations" ] } ## Define the variables and given values $$ \begin{aligned} &\text{Initial amount} = 75\ &\text{Regular price of shoes} = x\ &\text{Sale price of shoes} = \frac{1}{2}x\ &\text{Price of socks} = 6\ &\text{Remaining amount} = 32 \end{aligned} $$ ## Formulate the equation representing the total budget $$ \begin{aligned} &\text{Sale price of shoes} + \text{Price of socks} + \text{Remaining amount} = \text{Initial amount}\ &\frac{1}{2}x + 6 + 32 = 75 \end{aligned} $$

(A) $x + 6 + 32 = 75$

(B) $x + 6 = 32$

(C) $\frac{1}{2}x + 6 + 32 = 75$

(D) $\frac{1}{2}x + 32 = 75$

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

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Question

Explanation:

Define the variables and given values

Formulate the equation representing the total budget

Answer: