Straight Lines And Pair Of Straight Lines

A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2 : 1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (\(\alpha\), \(\beta\)). Then, the value of 7\(\alpha\) + 3\(\beta\) is equal to ____________.