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x = numero buscado
x/3 = tercer parte del numero
x/2 = mitad del numero
Ahora planteemos los datos del problema en una ecuacion:
x/3 + x/2 = 35
x(2) + 3(x)/3(2) = 35
2x + 3x/6 = 35
5x/6 = 35
5x = 6(35)
5x = 210
x = 210/5
x = 42
Verificamos:
x/3 + x/2 = 35
42/3 + 42/2 = 35
14 + 21 = 35
35 = 35
Por tanto el numero buscado es el 42
Espero ayude