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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Market Equilibrium", "Demand Curve Analysis", "Supply Curve Analysis" ], "new_concepts": [], "current_concepts": [ "Market Equilibrium", "Demand Curve Analysis", "Supply Curve Analysis" ] } ## Set supply equal to demand 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 $$ \begin{aligned} 94 + 160 &= 3p + \frac{5}{9}p \ 254 &= \frac{32}{9}p \ p &= \frac{254 \times 9}{32} \ p &= \frac{2286}{32} = 71.4375 \end{aligned} $$ ## Calculate the equilibrium demand Using the *Demand Curve Analysis* and *Supply Curve Analysis* knowledge points $$ \begin{aligned} D &= -\frac{5}{9}(71.4375) + 94 \ D &= -39.6875 + 94 \ D &= 54.3125 \approx 54 \end{aligned} $$

a. 151

b. 104

c. 71

d. 54

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QUESTION IMAGE

Question

Explanation:

Set supply equal to demand

Solve for the equilibrium price

Calculate the equilibrium demand

Answer: