below are the supply and demand equations for stereo headphones in a certain market. in these equations, p represents price, d represents demand, and s represents supply.
\d = \frac{-5}{9}p + 94\
\s = 3p - 160\
what is d at the point of equilibrium, to the nearest whole number?
a. 151
b. 104
c. 71
d. 54

Question

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": [ "Market Equilibrium" ], "new_concepts": [], "current_concepts": [ "Market Equilibrium", "Demand Curve Analysis", "Supply Curve Analysis" ] } ## Set up the equilibrium condition Using the *Market Equilibrium* knowledge point $$ \begin{aligned} &D = S \ &-\frac{5}{9}p + 94 = 3p - 160 \end{aligned} $$ ## Solve for the equilibrium price Using the *Market Equilibrium* knowledge point $$ \begin{aligned} &94 + 160 = 3p + \frac{5}{9}p \ &254 = \frac{32}{9}p \ &p = \frac{254 \times 9}{32} = \frac{2286}{32} = 71.4375 \end{aligned} $$ ## Calculate the equilibrium demand Using the *Market Equilibrium* knowledge point $$ \begin{aligned} &D = 3(71.4375) - 160 \ &D = 214.3125 - 160 = 54.3125 \ &D \approx 54 \end{aligned} $$

a. 151

b. 104

c. 71

d. 54

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Market Equilibrium" ] }

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Question

Explanation:

Set up the equilibrium condition

Solve for the equilibrium price

Calculate the equilibrium demand

Answer: