Question

La suma de las edades de A y B es de 84 años, y B tiene 8 años menos que A. Hallar ambas edades.
ECUACION DE PRIMER GRADO.
ES QUE QUIERO VERIFICAR SI ME QUEDARON BIEN. GRACIAS

Answer 1

$Hola~~~\mathbb{LI} \\ \\Nos~indica~que: \\ \\ \underbrace{La~suma~de~las~edades~de~A~y~B}_{A+B}~\underbrace{es}_{=}~\underbrace{de~84a\tilde{n}os}_{84} \\ \\ Entonces~la~ecuaci\acute{o}n~es: \\ \\ A+B=84~~-----\ \textgreater \ (I) \\ \\ \mathbb{qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq} \\ La~otra~indica: \\ \\ \underbrace{ B}_{B}~\underbrace{tiene}_{=}~\underbrace{8 a\tilde{n}os~menos~que~A}_{A-8}$

$La~ecuaci\acute{o}n~seria: \\ \\ B=A-8~~------\ \textgreater \ (II) \\ \\ \mathbb{ppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp} \\ Ahora~reemplazamos~(II)~en~(I)~vea: \\ \\ A+B=84~~--\ \textgreater \ siendo[B=A-8] \\ \\ A+A-8=84 \\ \\ 2A=92 \\ \\ \boxed{\boxed{A=46}}~~~---\ \textgreater \ a\tilde{n}os$

$Como~sabemos~el~valor~de~(A)~es~s\acute{o}lo~reemplazarlos~en~una~de \\ las~ecuaciones~para~calcular~el~valor~de (B), en~mi~caso~reemplazar\acute{e} \\ en~la~(II)~vea: \\ \\ B=A-8~~~--\ \textgreater \ Tenemos~[A=46] \\ \\ B=46-8 \\ \\ \boxed{\boxed{B=38}}~~--\ \textgreater \ a\tilde{n}os\\ \\ \\ \mathbb{qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq} \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~te~sirva, saludos!!$