La suma de tres numeros es 37. El menor disminuido en 1 equivale a 1/3 de la suma del mayor y el mediano; la diferencia del mediano y el menor equivale al mayor disminuido en 13. ¿Cuáles son los números? Por favor, necesito la respuesta :')
yexs
![======================================= \\ La~diferencia~del~mediano~y~el~menor~equivale~al~mayor~disminuido \\ en~13 \\ \\ y-x=z-13 \\\boxed{ y-z=x-13}~-------\ \textgreater \ (III) \\ \\ ===================================== \\ Para~calcular~(x)~reemplazemos~(II)~en~(I)~vea: \\ \\ x+y+z=37~~---\ \textgreater \ sabemos~que~[y+z=3x-3] \\ \\ x+\underbrace{y+z}_{3x-3}=37 \\ \\](https://tex.z-dn.net/?f=%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D+%5C%5C+La%7Ediferencia%7Edel%7Emediano%7Ey%7Eel%7Emenor%7Eequivale%7Eal%7Emayor%7Edisminuido+%5C%5C+en%7E13+%5C%5C++%5C%5C+y-x%3Dz-13+%5C%5C%5Cboxed%7B+y-z%3Dx-13%7D%7E-------%5C+%5Ctextgreater+%5C+%28III%29+%5C%5C++%5C%5C+%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D+%5C%5C+Para%7Ecalcular%7E%28x%29%7Ereemplazemos%7E%28II%29%7Een%7E%28I%29%7Evea%3A+%5C%5C++%5C%5C+x%2By%2Bz%3D37%7E%7E---%5C+%5Ctextgreater+%5C+sabemos%7Eque%7E%5By%2Bz%3D3x-3%5D+%5C%5C++%5C%5C+x%2B%5Cunderbrace%7By%2Bz%7D_%7B3x-3%7D%3D37+%5C%5C++%5C%5C++ "======================================= \\ La~diferencia~del~mediano~y~el~menor~equivale~al~mayor~disminuido \\ en~13 \\ \\ y-x=z-13 \\\boxed{ y-z=x-13}~-------\ \textgreater \ (III) \\ \\ ===================================== \\ Para~calcular~(x)~reemplazemos~(II)~en~(I)~vea: \\ \\ x+y+z=37~~---\ \textgreater \ sabemos~que~[y+z=3x-3] \\ \\ x+\underbrace{y+z}_{3x-3}=37 \\ \\")
![x+3x-3=37 \\ \\ 4x=40 \\ \\\boxed{\boxed{ x=10}}~~---\ \textgreater \ valor~de~(x) \\ \\ ===================================== \\ ahora~sumemos~(II)~y~(III)~vea: \\ \\ ~~~~~~~~~+\begin{cases}y+\not z=3x-3 \\ y-\not z=x-13 \\ \overline{~2y=4x-16~}\end{cases} \\ reemplazemos~el~valor~de~[x=10], tenemos~el~valor~de~(y)~vea \\ 2y=4x-16~~---\ \textgreater \ donde~[x=10]\\ \\](https://tex.z-dn.net/?f=x%2B3x-3%3D37++%5C%5C++%5C%5C+4x%3D40+%5C%5C++%5C%5C%5Cboxed%7B%5Cboxed%7B+x%3D10%7D%7D%7E%7E---%5C+%5Ctextgreater+%5C+valor%7Ede%7E%28x%29+%5C%5C++%5C%5C+%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D+%5C%5C+ahora%7Esumemos%7E%28II%29%7Ey%7E%28III%29%7Evea%3A+%5C%5C++%5C%5C+%7E%7E%7E%7E%7E%7E%7E%7E%7E%2B%5Cbegin%7Bcases%7Dy%2B%5Cnot+z%3D3x-3+%5C%5C+y-%5Cnot+z%3Dx-13+%5C%5C+%5Coverline%7B%7E2y%3D4x-16%7E%7D%5Cend%7Bcases%7D+%5C%5C+reemplazemos%7Eel%7Evalor%7Ede%7E%5Bx%3D10%5D%2C+tenemos%7Eel%7Evalor%7Ede%7E%28y%29%7Evea+%5C%5C+2y%3D4x-16%7E%7E---%5C+%5Ctextgreater+%5C+donde%7E%5Bx%3D10%5D%5C%5C++%5C%5C++ "x+3x-3=37 \\ \\ 4x=40 \\ \\\boxed{\boxed{ x=10}}~~---\ \textgreater \ valor~de~(x) \\ \\ ===================================== \\ ahora~sumemos~(II)~y~(III)~vea: \\ \\ ~~~~~~~~~+\begin{cases}y+\not z=3x-3 \\ y-\not z=x-13 \\ \overline{~2y=4x-16~}\end{cases} \\ reemplazemos~el~valor~de~[x=10], tenemos~el~valor~de~(y)~vea \\ 2y=4x-16~~---\ \textgreater \ donde~[x=10]\\ \\")
![2y=4(10)-16 \\ \\ 2y=24 \\ \\ \boxed{\boxed{y=12}}~---\ \textgreater \ valor~de~(y) \\ \\ ===================================== \\ Ahora~podemos~reemplazar~tanto~el~valor~de~(x)~y~(y)~en~una~de~las~ \\ ecuaciones~ya~sea~en~(I)~,(II)~o~(III), para~calular~(z), el~valor~debe \\ ser~lo~mismo~para~(z), en~mi~caso~voy~subtituir~en~(I)~vea: \\ x+y+z=37~~--\ \textgreater \ tenemos~que~[x=10~,~y=12] \\ \\ 10+12+z=37 \\ \\ 22+z=37\\ \\](https://tex.z-dn.net/?f=2y%3D4%2810%29-16++%5C%5C++%5C%5C+2y%3D24+%5C%5C++%5C%5C+%5Cboxed%7B%5Cboxed%7By%3D12%7D%7D%7E---%5C+%5Ctextgreater+%5C+valor%7Ede%7E%28y%29+%5C%5C++%5C%5C+%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D+%5C%5C+Ahora%7Epodemos%7Ereemplazar%7Etanto%7Eel%7Evalor%7Ede%7E%28x%29%7Ey%7E%28y%29%7Een%7Euna%7Ede%7Elas%7E+%5C%5C+ecuaciones%7Eya%7Esea%7Een%7E%28I%29%7E%2C%28II%29%7Eo%7E%28III%29%2C+para%7Ecalular%7E%28z%29%2C+el%7Evalor%7Edebe+%5C%5C+ser%7Elo%7Emismo%7Epara%7E%28z%29%2C+en%7Emi%7Ecaso%7Evoy%7Esubtituir%7Een%7E%28I%29%7Evea%3A+%5C%5C+x%2By%2Bz%3D37%7E%7E--%5C+%5Ctextgreater+%5C+tenemos%7Eque%7E%5Bx%3D10%7E%2C%7Ey%3D12%5D+%5C%5C++%5C%5C+10%2B12%2Bz%3D37+%5C%5C++%5C%5C+22%2Bz%3D37%5C%5C++%5C%5C++ "2y=4(10)-16 \\ \\ 2y=24 \\ \\ \boxed{\boxed{y=12}}~---\ \textgreater \ valor~de~(y) \\ \\ ===================================== \\ Ahora~podemos~reemplazar~tanto~el~valor~de~(x)~y~(y)~en~una~de~las~ \\ ecuaciones~ya~sea~en~(I)~,(II)~o~(III), para~calular~(z), el~valor~debe \\ ser~lo~mismo~para~(z), en~mi~caso~voy~subtituir~en~(I)~vea: \\ x+y+z=37~~--\ \textgreater \ tenemos~que~[x=10~,~y=12] \\ \\ 10+12+z=37 \\ \\ 22+z=37\\ \\")
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