WRITE AND SOLVE INVERSE VARIATION EQUATIONS

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.

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