Question

2)
Price varies directly as demand and inversely as the square root of supply. For demand = 1000
supply = 100, price = 500. Find the price, if demand = 3000 and supply = 900.
1) 100
2) 150
4) 250
3) 500​

Answer 1

Answer:

150 , because of math common sence

Answer 2

Option 3: 500 is the value of the price

Explanation:

Given that the price varies directly as demand and inversely as the square root of supply.

This can be written as the expression $P=\frac{kD}{\sqrt{S} }$

where P is the price, k is the constant, D is the demand and S is the supply

Also, given that Demand = 1000, Supply = 100 and Price = 500.

Let us substitute these values in the expression $P=\frac{kD}{\sqrt{S} }$ , we have,

$500=\frac{k(1000)}{\sqrt{100} }$

$500=\frac{k(1000)}{10 }$

$500=k(100)$

  $5=k$

Thus, the value of the constant k is 5

Now, we need to find the value of price when demand = 3000 and supply = 900

The value of price can be determined by substituting demand = 3000, supply = 900 and the constant k = 5

Thus, we have,

$P=\frac{5(3000)}{\sqrt{900} }$

$P=\frac{15000}{30 }$

$P=500$

Thus, the value of the price is 500

Therefore, Option 3 is the correct answer.

Learn more:

(1) Y varies directly as square root of x. When x = 16, y = 24. Find the constant of variation and equation of variation.

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