Question

If x and y vary inversely as each other and

(i) x = 3 when y = 8, find y when x = 4

(ii) x = 5, when y = 15, find x when y = 12

(iii) x = 30, find y when constant of variation = 900

(iv) y = 35, find x when constant of variation = 7

Answer 1

(i) Let y is p

x	3	4
y	8	p

3 x 8 = 4 x p

p = \(\frac{3\times 8}{4}\) = 6

x = 6

Therefore y is 6

(ii) Let x is p

x	5	p
y	15	12

5 x 15 = p x 12

p = \(\frac{5\times 15}{12}\) = \(\frac{25}{4}\)

x = \(\frac{25}{4}\)

Therefore x is \(\frac{25}{4}\)

(iii) Let y is p

Constant of variation is 900

30 x p = 900

p = \(\frac{900}{30}\) = 30

p = 30

Therefore p is 30

(iv) Let x is p

Constant of variation is 7

35 x p = 7

p = \(\frac{7}{35}\) = \(\frac{1}{5}\) 

p = \(\frac{1}{5}\)

Therefore x is \(\frac{1}{5}\)