Question

In each example, find the constant of proportionality and write the equation of variation.

(1) $y\mathrm{\alpha }\frac{1}{x}$. When y = 15, x = 14
(2) $z\mathrm{\alpha }\frac{1}{w}$. When w = 24, z = 2.5
(3) $s\mathrm{\alpha }\frac{1}{t}$. When t = 5.5, s = 4.4

Answer 1

(1) y and x are inversely related; when y is 15, x is 14.
∴ x y = k =15 × 14
⇒ k = 210
So, the constant of proportionality is 210.
The equation of variation can be written as: x y = 210.

(2) z and w are inversely related; when w is 24, x is 2.5 .
∴ z w = k =24 × 2.5
⇒ k = 60
So, the constant of proportionality is 60.
The equation of variation can be written as: zw = 60.

(3) s and t are inversely related; when s is 5.5, t is 4.4 .
∴s t = k =5.5×4.4
⇒ k = 24.2
So, the constant of proportionality is 24.2 .
The equation of variation can be written as: s t = 24.2 .