below are the supply and demand equations for umbrellas in a certain market. in these equations, p represents price, d represents demand, and s represents supply.
\d = -\frac{4}{3}p + 22\
\s = 3p - 36\
what is p at the point of equilibrium, to the nearest tenth?
a. 19.3
b. 16.5
c. 13.4
d. 12.0

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 supply equal to demand Using the *Market Equilibrium* knowledge point $$ \begin{aligned} D &= S \ -\frac{4}{3}p + 22 &= 3p - 36 \end{aligned} $$ ## Clear the fraction Multiply all terms by 3 to eliminate the denominator: $$ -4p + 66 = 9p - 108 $$ ## Isolate the variable p Rearrange the terms to solve for $p$: $$ \begin{aligned} 66 + 108 &= 9p + 4p \ 174 &= 13p \end{aligned} $$ ## Calculate the equilibrium price Divide both sides by 13 and round to the nearest tenth: $$ \begin{aligned} p &= \frac{174}{13} \ p &\approx 13.3846 \ p &\approx 13.4 \end{aligned} $$

a. 19.3

b. 16.5

c. 13.4

d. 12.0

{ "subject": "Business", "question_type": "Multiple Choice", "knowledge_point": [ "Business", "Economics", "Market Equilibrium" ] }

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QUESTION IMAGE

Question

Explanation:

Set supply equal to demand

Clear the fraction

Isolate the variable p

Calculate the equilibrium price

Answer: