Given: \(z − y = 14\)
Add \(y\) to both sides of the equation to get: \(z = y + 14\)

If \(x\), \(y\), and \(z\), are in the ratio \(1:3:5,\) then we know that: \(\frac{z}{y} = \frac{5}{3}\)

Now replace \(z\) with \(y+14\) to get: \(\frac{y+14}{y} = \frac{5}{3}\)

Cross multiply to get: \(3y + 42 = 5y\)

Solve: \(y = 21\)

To find the value of \(z\), we can use the fact that \(z − y = 14\)
Plug in \(y = 21\) to get: \(z - 21 = 14\)
Solve: \(z = 35\)


Finally, the given information tells us that \(\frac{x}{y} = \frac{1}{3}\)

Plug in \(y = 21\) to get: \(\frac{x}{21} = \frac{1}{3}\)

Solve to get: \(x = 7\)

So, \(x + y + z = 7 + 21 + 35 = 63\)

Answer: 63