Las edades de 4 hermanos son proporcionales a 2, 3, 4, 5 hallar la edad del menor si el promedio de todas la edades es igual a 21?

<img src="https://tex.z-dn.net/?f=Hola~~Anthony%20%5C%5C%20%0A" />

<img src="https://tex.z-dn.net/?f=%5Cboxed%7BLos~4~hermanos%7D%5Cbegin%7Bcases%7Dhermano%281%29---%5C%20%5Ctextgreater%20%5C%20a%3D%20%5Cfrac%7Ba%7D%7B2%7D%20%20%5C%5C%20hermano%282%29---%5C%20%5Ctextgreater%20%5C%20b%3D%20%5Cfrac%7Bb%7D%7B3%7D%20%20%5C%5C%20hermano%283%29---%5C%20%5Ctextgreater%20%5C%20c%3D%20%5Cfrac%7Bc%7D%7B4%7D%20%20%5C%5C%20hermano%284%29---%5C%20%5Ctextgreater%20%5C%20d%3D%20%5Cfrac%7Bd%7D%7B5%7D%20%5Cend" />

<img src="https://tex.z-dn.net/?f=Ahora~las~edades~proporcionales~de~los~4%20~hermanos~hacemos~igual~a%20%5C%5C%20un~constante~%28k%29~vea%3A%20%5C%5C%20%5C%5C%20%20%20%5Cfrac%7Ba%7D%7B2%7D%3D%20%5Cfrac%7Bb%7D%7B3%7D%3D%20%5Cfrac%7Bc%7D%7B4%7D%20%20%20%3D%20%5Cfrac%7Bd%7D%7B5%7D%20%3Dk%20%20%5C%5C%20%5C%5C%20%3D%5C%20%5Ctextgreater%20%5C%20a%3D2k%20%5C%5C%20~~~~~~~b%3D3k%20%5C%5C%20~~~~~~~c%3D4k%20%5C%5C%20~~~~~~~d%3D5k%20%5C%5C%20%20%5C%5C%20Y~sabemos~que~el~promedio~de~todas~las~edades~es~igual~a~21%20%5C%5C%20%20%5C%5C%20%20------------------------------------------------------------------------------------------%5C%5C%20%5Btex%5DLa~edad~promedio~seria%20%5C%5C%20%20%5C%5C%20%5Cboxed%7Bpromedio%3D%20%5Cfrac%7B%5Csum_%7Bi%7D%5E4%7D%7B4%7D%7D%20~~---%5C%20%5Ctextgreater%20%5C%20onde~%5Bpromedio%3D21%5D~entonces~tenemos%3A%20%5C%5C%20%20%5C%5C%2021%3D%20%5Cfrac%7B2k%2B3k%2B4k%2B5k%7D%7B4%7D%20%20%5C%5C%20%20%5C%5C%2021.4%3D14k~~---%5C%20%5Ctextgreater%20%5C%20despejando~%28k%29~tenemos%3A%20%5C%5C%20%20%5C%5C%20k%3D%20%5Cfrac%7B21.4%7D%7B14%7D%20~~---%5C%20%5Ctextgreater%20%5C%20simplificando~queda%3A%20%5C%5C%20%20%5C%5C%20%5Cboxed%7Bk%3D6%7D" />

<img src="https://tex.z-dn.net/?f=Ahora~ya~que~sabemos~que~el~menor~es%3A%20%5C%5C%20a%3D2k~~~--%5C%20%5Ctextgreater%20%5C%20se~sabe~el~valor~de~%5Bk%3D6%5D%2Creemplando~tenemos%3A%20%5C%5C%20%20%5C%5C%20a%3D2.6%20%5C%5C%20%20%5C%5C%20%5Cboxed%7B%5Cboxed%7Ba%3D12%7D%7D--%5C%20%5Ctextgreater%20%5C%20edad~del~menor." /> = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Espero te sirva, saludos!