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Learning outcome: Solve a linear system of equations in two and three variables using algebraic methods. Read and solve word problems by modeling them with systems of linear equations. Activity: Let p represent the selling price for a bluetooth device. Suppose that the demand equation for this device can be modeled as the linear function D(p) = 200- 5p and that the supply equation for the same device as S(p) = 10p. Find the equilibrium price and quantity for this device keeping in mind that at market equilibrium demand equals supply.

Respuesta :

Answer: Equilibrium price would be $13.33 and equilibrium quantity  would be 133.3 units.

Step-by-step explanation:

Since we have given that

Demand function is stated as

[tex]D(p)=200-5p[/tex]

Supply function is stated as

[tex]S(p)=10p[/tex]

We need to find the equilibrium price and quantity for this device.

For equilibrium, D(p) = S(p).

so, it becomes,

[tex]200-5p=10p\\\\200=10p+5p\\\\200=15p\\\\p=\dfrac{200}{15}\\\\p=\$13.33[/tex]

and when we put the value of p in any function:

[tex]Q=10\times 13.33=133.3\ units[/tex]

Hence, Equilibrium price would be $13.33 and equilibrium quantity  would be 133.3 units.

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