Question Number 39814 by pieroo last updated on 11/Jul/18
$$\mathrm{kwame},\:\mathrm{ama}\:\mathrm{and}\:\mathrm{yaw}\:\mathrm{shared}\:\mathrm{an}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{money} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{3}:\mathrm{4}:\mathrm{5}.\:\mathrm{if}\:\mathrm{ama}\:\mathrm{had}\:\$\mathrm{8},\mathrm{400}\:\mathrm{more}\:\mathrm{than}\:\mathrm{kwame}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{total}\:\mathrm{amount}\:\mathrm{shared}. \\ $$
Answered by ajfour last updated on 11/Jul/18
$${K}=\mathrm{3}{x}\:\:,\:{A}=\mathrm{4}{x}\:,\:{Y}=\mathrm{5}{x} \\ $$$$\mathrm{4}{x}\:=\:\mathrm{3}{x}+\$\mathrm{8400} \\ $$$$\Rightarrow\:\:{x}=\:\$\:\mathrm{8400} \\ $$$${T}\:=\:{K}+{A}+{Y}\:=\:\mathrm{12}{x} \\ $$$${T}\:=\:\mathrm{12}×\$\:\mathrm{8400}\:=\:\$\:\mathrm{100},\mathrm{800}\:. \\ $$
Commented by pieroo last updated on 11/Jul/18
$$\mathrm{thanks},\:\mathrm{but}\:\mathrm{what}\:\mathrm{does}\:\mathrm{the}\:\mathrm{x}\:\mathrm{stand}\:\mathrm{for}? \\ $$
Answered by MrW3 last updated on 11/Jul/18
$$\mathrm{3}+\mathrm{4}+\mathrm{5}=\mathrm{12} \\ $$$${if}\:\$\mathrm{12}\:{were}\:{to}\:{be}\:{shared},\:{then}\:{K}\:{gets}\: \\ $$$$\$\mathrm{3},\:{A}\:{gets}\:\$\mathrm{4}\:{and}\:{Y}\:{gets}\:\$\mathrm{5}.\:{I}.{e}.\:{A}\:{gets}\: \\ $$$$\$\mathrm{1}\:{more}\:{than}\:{K}.\:{So}\:{that}\:{A}\:{gets}\:\$\mathrm{8400} \\ $$$${than}\:{K},\:{the}\:{total}\:{money}\:{to}\:{be}\:{shared} \\ $$$${must}\:{be}\:\mathrm{12}×\mathrm{8400}=\$\mathrm{100800}. \\ $$