If $5A=6B=9C$, what is $A:B:C$?

Given relation:
$$5A=6B=9C$$
To find the ratio $A:B:C$, let $5A=6B=9C=k$.Then:
$$A=\frac{k}{5},B=\frac{k}{6},C=\frac{k}{9}$$
The ratio is:
$$A:B:C=\frac{1}{5}:\frac{1}{6}:\frac{1}{9}$$
To convert this fraction ratio into whole numbers, multiply each term by the Least Common Multiple (LCM) of the denominators $(5,6,9)$.
$$\text{LCM}(5,6,9)=90$$
Now, multiply each term by $90$:
$$A=\frac{1}{5}\times 90=18$$
$$B=\frac{1}{6}\times 90=15$$
$$C=\frac{1}{9}\times 90=10$$
Therefore, $A:B:C=18:15:10$.