Tìm các số \(x,y,z\), biết:

d) \(\frac{x}{2} = \frac{y}{3};\frac{y}{4} = \frac{z}{5}\) và \(x - y - z = 28\);

d) \(\frac{x}{2} = \frac{y}{3}\,;\,\,\frac{y}{4} = \frac{z}{5}\) và \(x - y - z = 28\)

\(\frac{x}{2} = \frac{y}{3}\) suy ra \(x = \frac{{2y}}{3}\)

\(\frac{y}{4} = \frac{z}{5}\) suy ra \(z = \frac{{5y}}{4}\)

Ta có \(x - y - z = 28\)

\(\frac{{2y}}{3} - y - \frac{{5y}}{4} = 28\)

\( - \frac{{19}}{{12}}y = 28\) suy ra \(y = 28:\left( { - \frac{{19}}{{12}}} \right)\)

do đó \(y = \frac{{ - 336}}{{19}}\).

Ta có: \(x = \frac{{2y}}{3}\)

\(x = \frac{2}{3}.\left( {\frac{{ - 336}}{{19}}} \right)\) suy ra \(x = \frac{{ - 224}}{{19}}\)

Ta có: \(z = \frac{{5y}}{4}\)

\(z = \frac{5}{4}.\left( {\frac{{ - 336}}{{19}}} \right)\)

\(z = \frac{{ - 420}}{{19}}\)