Question

3. If x is inversely proportional to y and x = 40 when
y = 5, find
() the value of x when y = 25,
(ii) an equation connecting x and y.
(iii) the value of y when x = 400.​

Answer 1

SOLUTION

GIVEN

x is inversely proportional to y and x = 40 when y = 5

TO DETERMINE

(i) The value of x when y = 25

(ii) An equation connecting x and y

(iii) The value of y when x = 400

EVALUATION

Here it is given that x is inversely proportional to y

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

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

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

Now x = 40 when y = 5

$\displaystyle \sf{ \implies \: 40 \times 5 = k }$

$\displaystyle \sf{ \implies \: k = 200 }$

So the above becomes

$\displaystyle \sf{ \implies \: xy = 200 }$

(i) when y = 25

$\displaystyle \sf{ \: xy = 200 \: \: \: gives }$

$\displaystyle \sf{ \implies \: x= \frac{200}{25} = 8 }$

Hence the required value of x = 8

(ii) An equation connecting x and y is

$\displaystyle \sf{ xy = 200 \: }$

(iii) when x = 400

$\displaystyle \sf{ \implies \: xy = 200 \: \: \: gives }$

$\displaystyle \sf{ \implies \: 400y = 200 \: \: }$

$\displaystyle \sf{ \implies \: y = \frac{200}{400} \: \: \: }$

$\displaystyle \sf{ \implies \: y = \frac{1}{2} \: \: \: }$

Hence the required value of y is

$\displaystyle \sf{ \frac{1}{2} \: \: \: }$

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Answer 2

x is inversely proportional to y and x = 40 when y = 5