Question Number 177179 by Mastermind last updated on 01/Oct/22
$$\mathrm{If}\:\mathrm{a}\:\mathrm{number}\:\mathrm{is}\:\mathrm{20\%}\:\mathrm{more}\:\mathrm{the}\:\mathrm{other},\:\mathrm{how} \\ $$$$\mathrm{much}\:\mathrm{percent}\:\mathrm{is}\:\mathrm{the}\:\mathrm{second}\:\mathrm{number} \\ $$$$\mathrm{less}\:\mathrm{than}\:\mathrm{the}\:\mathrm{first}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}! \\ $$
Commented by Frix last updated on 02/Oct/22
$$\mathrm{it}'\mathrm{s}\:\mathrm{simply}\:\mathrm{multiplying}\:\mathrm{and}\:\mathrm{dividing} \\ $$$${x}+\mathrm{20\%}={y}\:\overset{\mathrm{1}+\frac{\mathrm{20}}{\mathrm{100}}=\mathrm{1}.\mathrm{2}} {\Leftrightarrow}\:\mathrm{1}.\mathrm{2}{x}={y} \\ $$$$\Rightarrow \\ $$$${x}=\frac{{y}}{\mathrm{1}.\mathrm{2}}\:\Leftrightarrow\:{x}=.\mathrm{8}\bar {\mathrm{3}}{y}\:\overset{\mathrm{1}−\frac{\mathrm{16}.\bar {\mathrm{6}}}{\mathrm{100}}=.\mathrm{8}\bar {\mathrm{3}}} {\Leftrightarrow}\:{y}−\mathrm{16}.\bar {\mathrm{6}\%}={x} \\ $$
Answered by JDamian last updated on 01/Oct/22
$${b}={a}+{a}\frac{\mathrm{20}}{\mathrm{100}}=\mathrm{1}.\mathrm{2}{a} \\ $$$$ \\ $$$$\frac{{b}−{a}}{{b}}×\mathrm{100}=\frac{\mathrm{1}.\mathrm{2}{a}−{a}}{\mathrm{1}.\mathrm{2}{a}}×\mathrm{100}= \\ $$$$=\frac{\mathrm{1}.\mathrm{2}−\mathrm{1}}{\mathrm{1}.\mathrm{2}}×\mathrm{100}=\frac{\mathrm{0}.\mathrm{2}}{\mathrm{1}.\mathrm{2}}×\mathrm{100}=\frac{\mathrm{20}}{\mathrm{1}.\mathrm{2}}=\mathrm{16}.\hat {\mathrm{6}\%} \\ $$
Commented by Mastermind last updated on 02/Oct/22
$$\mathrm{correct}\:\mathrm{that}\:\mathrm{what}\:\mathrm{i}\:\mathrm{got}\:\mathrm{here},\:\mathrm{thanks}\:\mathrm{man} \\ $$
Commented by peter frank last updated on 02/Oct/22
$$\mathrm{thanks} \\ $$