Question

La razón aritmética de dos números es 15 y su razón geométrica es 2 1/2. hallar al mayor de los dos números.

Answer 1

$Hola~~~\mathbb{WAHIRY} \\ \\ sean~dos~n\acute{u}meros \begin{cases}~~~---\ \textgreater \ a_1 \\ ~~~---\ \textgreater \ a_2\end{cases} \\ \\Su~ raz\acute{o}n~aritm\acute{e}tica \\ \boxed{a_2-a_1=15}~--->(I) \\ \\ Su~raz\acute{o}n~geom\acute{e}tico \\ \frac{a_2}{a_1}=2 \frac{1}{2}~~~--\ \textgreater \ tenemos~[2 \frac{1}{2}= \frac{5}{2} ] \\ \\ \frac{a_2}{a_1}= \frac{5}{2} ~~--\ \textgreater \ despejando~(a_2) \\ \\ \boxed{a_2= \frac{5a_1}{2} }~---\ \textgreater \ (II)$

$Reemplazamos~(II)~en~(I) ~tenemos: \\ \\ a_2-a_1=15~~~--\ \textgreater \ [a_2= \frac{5a_1}{2} ], reemplazando \\ \\ \frac{5a_1}{2}-a_1=15 \\ \\ 5a_1-2a_1=30 \\ \\ 3a_1=30 \\ \\ \boxed{\boxed{a_1=10} } \\ \\ ===================================== \\ Ahora~reemplazamos~el~valor~de~(a_1=10)~en~una~de~las~ecuaciones \\ sea~en~(I)~o~(II)~~yo~voy~a~reemplazar~en~la~(I)~vea:$

$a_2-a_1=15~~~--\ \textgreater \ tenemos~[a_1=10], reemplazando~ \\ \\ a_2-10=15 \\ \\ a_2=15+10 \\ \\ \boxed{\boxed{a_2=25}} \\ \\ =================================== \\ Por~tanto~el~mayor~es: 25 \\ \\ \mathbb{tttttttttttttttttttttttttttttttttttt}\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~te~sirva~saludos!!$