Question

A student was 4/5ths as old in 2010 as he will be in an additional 6 years. How old was Lady Gaga in 2010? (I can't download files because of low space)

Answer 1

let's say "x" is how old he will be in 2016, so in 2010, 6 years earlier, he's 4/5 ths of that age in 2016, or namely in 2010 he's (4/5)x.  Since we know his total age in 2016 is "x", then if we just add 6 more years to (4/5)x, we'll get his age in 2016, or

$\stackrel{\textit{age in 2010}}{\cfrac{4}{5}x}~~ +~~\stackrel{years}{6}~~ =~~\stackrel{\textit{age in 2016}}{x} \\\\\\ \stackrel{\textit{let's multiply both sides by }\stackrel{LCD}{5}}{5\left( \cfrac{4x}{5}+6 \right)=5(x)}\implies 4x+30=5x\implies \stackrel{\textit{age in 2016}}{\boxed{30=x}} \\\\\\ \stackrel{~\hfill \textit{age in 2010}}{\cfrac{4}{5}(30)\implies \boxed{24}}$