Question

Point C ∈

AB
, AB = 30m. Point C is 1.5 times farther from point A than from point B. Find AC and CB

Answer 1

`\bf A\underset{\textit{1.5 times farther than CB}}{\stackrel{1.5x}{\rule[0.35em]{15em}{0.25pt}}}C\stackrel{x}{\rule[0.35em]{10em}{0.25pt}}B \\\\\\ AB=AC+CB\implies \stackrel{AB}{30}=\stackrel{AC}{1.5x}+\stackrel{CB}{x}\implies 30=2.5x \\\\\\ \cfrac{30}{2.5}=x\implies 12=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{AC}{1.5(12)}\implies 18~\hspace{10em}\stackrel{CB}{12}`