select the correct answer.

sam is an artist, and he wants to purchase frames to display his work at home. he wants to frame no fewer than 10 of his pieces and spend no more than $225. large frames cost $24, and medium frames cost $18.

which system of inequalities can sam use to determine the number of large frames, $x$, and medium frames, $y$, that he can purchase?

$\begin{aligned} &18x + 24y \le 225 \\ &x + y \ge 10 \end{aligned}$

$\begin{aligned} &24x + 18y \ge 225 \\ &x + y \le 10 \end{aligned}$

$\begin{aligned} &18x + 24y \ge 225 \\ &x + y \le 10 \end{aligned}$

$\begin{aligned} &24x + 18y \le 225 \\ &x + y \ge 10 \end{aligned}$

Question

select the correct answer.

sam is an artist, and he wants to purchase frames to display his work at home. he wants to frame no fewer than 10 of his pieces and spend no more than $225. large frames cost $24, and medium frames cost $18.

which system of inequalities can sam use to determine the number of large frames, $x$, and medium frames, $y$, that he can purchase?

$\begin{aligned} &18x + 24y \le 225 \\ &x + y \ge 10 \end{aligned}$

$\begin{aligned} &24x + 18y \ge 225 \\ &x + y \le 10 \end{aligned}$

$\begin{aligned} &18x + 24y \ge 225 \\ &x + y \le 10 \end{aligned}$

$\begin{aligned} &24x + 18y \le 225 \\ &x + y \ge 10 \end{aligned}$

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": [ "Systems of Linear Inequalities" ], "new_concepts": [], "current_concepts": [ "Systems of Linear Inequalities" ] } ## Define variables and quantity constraint Using the *Systems of Linear Inequalities* knowledge point $$ \begin{aligned} &x \ge 0, \quad y \ge 0 \ &x + y \ge 10 \end{aligned} $$ ## Define cost constraint Using the *Systems of Linear Inequalities* knowledge point $$ \begin{aligned} &\text{Cost of large frames: } 24x \ &\text{Cost of medium frames: } 18y \ &24x + 18y \le 225 \end{aligned} $$ ## Combine into system of inequalities Using the *Systems of Linear Inequalities* knowledge point $$ \begin{cases} 24x + 18y \le 225 \ x + y \ge 10 \end{cases} $$

(A) $18x + 24y \le 225$ $x + y \ge 10$

(B) $24x + 18y \ge 225$ $x + y \le 10$

(C) $18x + 24y \ge 225$ $x + y \le 10$

(D) $24x + 18y \le 225$ $x + y \ge 10$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Define variables and quantity constraint

Define cost constraint

Combine into system of inequalities

Answer: