Question

It is given that $l$ varies directly as $m$.
(i) Write an equation which relates $l$ and $m$.
(ii) Find the constant of proportion (k), when $l$ is $6$, then $m$ is $18$.
(iii) Find $l$, when $m$ is $33$.( take constant of proportion as 1/3)
(iv) Find $m$, when $l$ is $8$.
[3 marks]

Answer 1

(i) Since $l$ varies directly as $m$.
Equation related to $l$ and $m$ is
$\frac{l}{m}=k\left(constant\right)$

[0.5 mark]

(ii) Since $l$ varies directly as $m$.
If $l=6$ and $m=18$, then
$k=\frac{6}{18}=\frac{1}{3}$

[0.5 mark]

(iii) Given $m=33$,
$\frac{l}{m}=\frac{1}{3}...\left(1\right)$
Substituting the value of $m$ in (1)
$\Rightarrow \frac{l}{33}=\frac{1}{3}\Rightarrow l=\frac{33}{3}=11$

[1 mark]

(iv) Given $l=8$,
$\frac{l}{m}=\frac{1}{3}...\left(1\right)$
Substituting the value of $l$ in (1)
$\Rightarrow \frac{8}{m}=\frac{1}{3}\Rightarrow m=8\times 3=24$

[1 mark]