Question

la mitad de un numero mas su tercera parte es igual a su quinta parte aumentada en 10.¿cual es el numero?

Answer 1

Respuesta:

$\frac{300}{19}$

Explicación paso a paso:

$\frac{x}{2}+\frac{x}{3} = \frac{x}{5} +10\\\\\frac{(3x)+(2x)}{6} =\frac{x}{5} +10} \\\\\frac{5x}{6} -\frac{x}{5} =10 \\\\\\\frac{(25x)-(6x)}{30} =10\\\\\frac{19x}{30} =10\\\\19x =10(30)\\\\x=\frac{300}{19}$

Comprobar:

$\frac{\frac{300}{19} }{2}+\frac{\frac{300}{19} }{3} = \frac{\frac{300}{19} }{5} +10\\\\\frac{150}{19} +\frac{100}{19}=\frac{60}{19}+10\\\\\frac{250}{19} =\frac{60+(19*10)}{19}\\\\\frac{250}{19} =\frac{250}{19}$