1. The problem involves inverse proportionality, where two variables multiply to a constant. For example, if $g$ and $h$ are inversely proportional, then $g = \frac{k}{h}$ for some constant $k$. 2. Given $g = \frac{54}{h}$, we find $g$ when $h=9$ by substituting: $$g = \frac{54}{9} = 6$$ 3. For the printing problem, minutes $m$ and printers $n$ are inversely proportional, so: $$m = \frac{140}{n}$$ Calculate $m$ when $n=20$: $$m = \frac{140}{20} = 7$$ 4. For $a$ and $b$ inversely proportional with $a = \frac{30}{b}$, find $b$ when $a=5$: $$5 = \frac{30}{b} \implies b = \frac{30}{5} = 6$$ 5. For kettle boiling time $n$ and power $p$ inversely proportional: $$n = \frac{270}{p}$$ Given $n=90$, find $p$: $$90 = \frac{270}{p} \implies p = \frac{270}{90} = 3$$ 6. For $r$ and $t$ inversely proportional with $r = \frac{96}{t}$: a) Find $r$ when $t=4$: $$r = \frac{96}{4} = 24$$ b) Find $t$ when $r=8$: $$8 = \frac{96}{t} \implies t = \frac{96}{8} = 12$$ Inverse proportionality means as one variable increases, the other decreases such that their product is constant. Final answers: - $g=6$ when $h=9$ - $m=7$ when $n=20$ - $b=6$ when $a=5$ - $p=3$ when $n=90$ - $r=24$ when $t=4$ - $t=12$ when $r=8$