Question

If a and b vary inversely as each other and a = 16 when b = 4, find b
when a = 8.

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Answer 1

Answer:

I hope its help full for you

Answer 2

The value of b = 8

Given :

• a and b vary inversely as each other

• a = 16 when b = 4

To find :

The value of b when a = 8

Solution :

Step 1 of 3 :

Form the equation

Here it is given that a and b vary inversely as each other

$\displaystyle \sf{a \propto \: \frac{1}{b} }$

$\displaystyle \sf{ \implies \: a = \: \frac{k}{b} }$

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

Where k is a non zero real number

Step 2 of 3 :

Find the value of k

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

a = 16 when b = 4 gives

$\displaystyle \sf{ \implies \: (16 \times 4) = k }$

$\displaystyle \sf{ \implies \: k = 64 }$

Equation 1 gives

$\displaystyle \sf{ \implies \: ab = 64}$

Step 3 of 3 :

Find value of b when a = 8

$\displaystyle \sf{ \implies \: ab = 64}$

For x = 16 we have

$\displaystyle \sf{ \implies \: 8b = 64}$

$\displaystyle \sf{ \implies \: b = 8}$

Hence the required value of b = 8

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