Two companies produce the same product but at different rates. The equation \(P = x + y + 2z\) gives the total number of units produced by Company P, with \(x\) standing for hours, \(y\) standing for workers, and \(z\) standing for components. The equation \(M = 2x + y + 3z\) is used by Company M to calculate its total number of units produced.
If both companies use \(100\) hours, \(20\) workers, and five components, what is the total number of units produced?