Question

suppose y varies inversely with x.if y=150 when x =2,find y when x = 25

Answer 1

Answer: 12

Step-by-step explanation:

Answer 2

The value of y = 12

Given :

• x and y varies inversely as each other

• y = 150 when x = 2

To find :

The value of y when x = 25

Solution :

Step 1 of 3 :

Form the equation

Here it is given that x and y varies inversely as each other

$\displaystyle \sf{x \propto \: \frac{1}{y} }$

$\displaystyle \sf{ \implies \: x = \: \frac{k}{y} }$

$\displaystyle \sf{ \implies \: xy = k } \: \: \: \: - - - (1)$

Where k is a non zero real number

Step 2 of 3 :

Find the value of k

$\displaystyle \sf{ \implies \: xy = k } \: \: \: \: - - - (1)$

y = 150 when x = 2 gives

$\displaystyle \sf{ \implies \: (2 \times 150) = k }$

$\displaystyle \sf{ \implies \: k = 300 }$

Equation 1 gives

$\displaystyle \sf{ \implies \: xy = 300}$

Step 3 of 3 :

Find value of y when x = 25

$\displaystyle \sf{ \implies \: xy = 300}$

For x = 25 we have

$\displaystyle \sf{ \implies \: 25y = 300}$

$\displaystyle \sf{ \implies y = \frac{300}{25} }$

$\displaystyle \sf{ \implies \: y = 12}$

Hence the required value of y = 12

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