# WRITE AND SOLVE INVERSE VARIATION EQUATIONS

## About "Write and solve inverse variation equations"

Write and solve inverse variation equations :

Here we are going to see how to write and solve inverse variation equations from the given information.

Inverse variation :

If an increase () [decrease ()] in one quantity produces a proportionate decrease ([increase ()] in another quantity, then we say that the two quantities are in inverse variation.

Equation of inverse variation :

Direct variation can be represented by the equation

y = k/x

Here the variable "k" is known as the constant of variation, and it cannot equal to zero.

Let us look into some example problems to understand how to write and solve inverse variation equations.

## Write and solve inverse variation equations - Examples

Example 1 :

Assume that y varies inversely with x. If y = 1 when x = 6, find y when x = 3

Solution :

Equation of inverse variation :

y = k/x  ---------(1)

In order to find the value of "k" in the equation, we need to apply the values of x and y in the equation.

1  =  k (6)

1  =  6k

Divide by 6 on both sides

1/6  = 6k/6

1/6  =  k

k  =  1/6

By applying the value of k in the (1)st equation, we get

y = 6/x

Equation of inverse variation is y = 6/x.

From this we need to find the value of y, when x = 3.

y = 6/3 ===> 2

Hence the value of y = 2

Example 2 :

Assume that y varies inversely with x. If y = 50 when x = 40, find x when y = 250.

Solution :

Equation of inverse variation :

y = k/x  ---------(1)

In order to find the value of "k" in the equation, we need to apply the values of x and y in the equation.

50  =  k/40

Multiply by 40 on both sides,

50(40)  = (k/40) x 40

2000  =  k

k  =  2000

By applying the value of k in the (1)st equation, we get

y = 2000/x

Equation of inverse variation is y = 2000/x.

From this we need to find the value of x, when y = 250.

250 = 2000/x

Multiply by "x" on both sides

250x = 2000

Divide by 250 on both sides

250x/250  =  2000/250

x = 8

Hence the value of x = 8

Example 3 :

Assume that y varies inversely with x. If y = 50 when x = 8, find y when x = 200.

Solution :

Equation of inverse variation :

y = k/x  ---------(1)

In order to find the value of "k" in the equation, we need to apply the values of x and y in the equation.

50  =  k/8

Multiply by 8 on both sides,

50(8)  = (k/8) x 8

400  =  k

k  =  400

By applying the value of k in the (1)st equation, we get

y = 400/x

Equation of inverse variation is y = 400/x.

From this we need to find the value of y, when x = 200.

y = 400/200

y = 2

Hence the value of y is 2.

Example 4 :

Assume that y varies inversely with x.If y = 2 when x = 2, find y when x = 3.

Solution :

Equation of inverse variation :

y = k/x  ---------(1)

In order to find the value of "k" in the equation, we need to apply the values of x and y in the equation.

2  =  k /2

Multiply by 2 on both sides,

2(2)  =  (k/2) x 2

4  =  k

k  =  4

By applying the value of k in the (1)st equation, we get

y = 4/x

Equation of inverse variation is y = 4/x.

From this we need to find the value of y, when x = 3.

y = 4/3

Hence the value of y is 4/3.

After having gone through the stuff given above, we hope that the students would have understood "Write and solve inverse variation equations".

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