Question

el denominador de una fraccion propia es el quintuple del numerador, mas 7 unidades. si a la suma de los terminos de dicha fracción es 79, ¿cual es el valor de la raiz cuadrada del numerador aumentado en 4 unidades?

rpta: 4

Answer 1

$Hola~~ \\ \\ Vamos~llamar: \\ Numerador----\ \textgreater \ x \\ Denominador---\ \textgreater \ y \\ Entonces ~la~fracci\acute{o}n~seria~~----\ \textgreater \ \boxed{\frac{x}{y}} \\ \\ \mathbb{uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu} \\ \star~Ahora~vamos~a~las~condiciones~que~nos~dice: \\ \\ \underbrace{El~denominador}_{\mathbf{y}}~\underbrace{es}_{\mathbf{=}}~\underbrace{el~quintuplo~del~numerador}_{\mathbf{5x}},\underbrace{mas}_{\mathbf{+}}~\underbrace{7~unidades}_{\mathbf{7}}\\ \\ Entonces~la~ecuaci\acute{o}n~es:$

$\boxed{y=5x+7}~~-----\ \textgreater \ (I) \\ \\ \mathbb{uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu} \\ \star~La~otra~condici\acute{o}n~indica: \\ \\ \underbrace{La~suma~de~los~t\acute{e}rminos~de~dicha~fracci\acute{o}n}_{\mathbf{x+y}}~\underbrace{es}_{=}~\underbrace{79}_{\mathbf{79}} \\ \\ Nuestra~ecuaci\acute{o}n~es: \\ \\ \boxed{x+y=79}~~------(II) \\ \\ \mathbb{uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu} \\ Para~calcular~(~\mathbf{x})~reemplazaremos~(I)~en~(II)~vea:$

$x+y=79~~---\ \textgreater \ donde~[y=5x+7], reemplazando~en~(y) \\ \\ x+(5x+7)=79 \\ \\ 6x+7=79 \\ \\ 6x=72 \\ \\ \boxed{\boxed{x=12}} \\ \\ \mathbb{uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu} \\ Para~calcular~el~valor~de~(\mathbf{y})~podemos~reemplzar~el~valor~de~(x) \\ tanto~en~la~ecuaci\acute{o}n~(I) ~o~(II)~el ~valor ~del~resultado~ser\acute{a}~lo~ \\ mismo, en~mi~caso~reemplazare~en~la~(I)~vea:$

$y=5x+7~~---\ \textgreater \ donde[ x=12]~reemplazando~en~(x) \\ \\ y=5(12)+7 \\ \\ \boxed{\boxed{y=71} } \\ \\ \mathbb{uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu} \\ Nuestra~fracci\acute{o}n~es:--\ \textgreater \ \boxed{\frac{12}{71}} \\ \\ \star~respondiendo~la~pregunta: \\ \underbrace{El~valor~de~la~raiz~cuadrada~del~numerador~aumentado~en~4}_{\mathbf{ \sqrt{12+4} }} \\ \\ \sqrt{12+4}= \sqrt{16} =\boxed{\boxed{4}}---\ \textgreater \ respuesta$

$\mathbb{vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv} \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ te~sirva~saludos!!$

Answer 2

El numerador es N, entonces el denominador es 5N + 7.
La suma de términos es 79: N + (5N + 7) = 79
6N + 7 = 79
6N = 72
N = 12

El numerador aumentado 4 unidades: 12 + 4 = 16
La raíz cuadrada de 16 es 4

Respuesta: 4