Question

Two quantities vary inversely. If the value of the first is 15 when the value of the second is 18, find the value of the second quantity when the first is 10.. .

Answer 1

Answer:

The value of second quantity is 27

Step-by-step explanation:

Inverse variation can be represented by the equation xy=k or $y = \frac{k}{x}$ i.e,

y varies inversely as x , if there is some nonzero constant k such that, xy =k or $y = \frac{k}{x}$ where  x≠0 and y≠0.

Given: Two quantities vary inversely.

Let x be the first quantity and y be the second quantity if they  vary inversely.

then, by definition of inverse variation;

$y = \frac{k}{x}$            .....[1]

Substitute the value of x=15 and y=18 to solve for k;

$18= \frac{k}{15}$

Multiply both sides by 15 we have;

$15\times 18=15 \times \frac{k}{15}$

Simplify:

k=270

now, find  the second quantity y using same method when x=10.

then;

after substituting the value of x=10 and k=270 in [1] ;

$y = \frac{270}{10}$

Simplify:

y= 27

Therefore, the second quantity value i.e,y = 27

Answer 2

Y = k/x

15 = k/18

270 = k


10 = 270 /x

10 x =  270

x = 27

the second number is 27

hope this helps