the soccer team is planning to sell health bars for a fundraiser. the prices of purchasing health bars from two different companies are represented by the system of equations shown, where $x$ is the number of bars purchased and $y$ is the total cost in dollars.

company a: $y=0.75x$
company b: $y=10+0.50x$

how many bars would the team need to purchase from each company in order for the total cost to be equal?

6
8
30
40

Question

the soccer team is planning to sell health bars for a fundraiser. the prices of purchasing health bars from two different companies are represented by the system of equations shown, where $x$ is the number of bars purchased and $y$ is the total cost in dollars.

company a: $y=0.75x$
company b: $y=10+0.50x$

how many bars would the team need to purchase from each company in order for the total cost to be equal?

6
8
30
40

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Systems of Linear Equations", "Substitution Method" ], "new_concepts": [], "current_concepts": [ "Systems of Linear Equations", "Substitution Method", "Linear Modeling" ] } ## Set up the system of equations $$ \begin{aligned} y &= 0.75x \ y &= 10 + 0.50x \end{aligned} $$ ## Equate the expressions for y $$ 0.75x = 10 + 0.50x $$ ## Solve for x $$ \begin{aligned} 0.25x &= 10 \ x &= \frac{10}{0.25} \ x &= 40 \end{aligned} $$

6

8

30

40

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

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QUESTION IMAGE

Question

Explanation:

Set up the system of equations

Equate the expressions for y

Solve for x

Answer: