# Direct Variations (Sample Questions)

Example 1:
y varies directly to x3 and if y = 54 when x = 3, find
(a)  The value of when y = 16
(b)  The value of y when x = 4

Solution:
Given α x³ , y = kx³
When y = 54, x = 3,
54 = k (3)³
54 = 27k
k = 2
Therefore y = 2x³

(a) When y = 16
16 = 2x³
x³ = 8
x = 2

(b)
When x = 4
y = 2(4)³ = 128

Example 2:
Given that p varies directly as square root of q and p = 12 when = 36, find
(a) The value of p when = 16
(b) The value of q when = 18

Solution:

$\begin{array}{l}p\propto \sqrt{q},\text{}p=k\sqrt{q}\\ 12=k\sqrt{36}\end{array}$
12 = k(6)
k = 2
$p=2\sqrt{q}$

(a)
$\begin{array}{l}p=2\sqrt{q}\\ p=2\sqrt{16}\end{array}$
p = 8

(b)
$\begin{array}{l}p=2\sqrt{q}\\ 18=2\sqrt{q}\text{}\to 9=\sqrt{q}\end{array}$
9² = q
q = 81