help

The centroid of a triangle will divide the  triangle into  3  equal  areas

The coordinates of the  centroid are  given  by

;

 (  [sum of the  x coordinates of  the  vertex points ] / 3 , [ sum of the  y coordinates of the vertex points ] / 3 ) =

( [5 + 3 + 6 ]  /  3  , [ 8 + -2 + 1 ] / 3  )  =  (  14/3, 7/3)

So

10m + n   =

10 ( 14/3) + (7/3) =   140/3  +  7/3   = 147/3   =   49

Triangle ABC has vertices at A(5,8), B(3,-2), and C(6,1). The point D with coordinates (m,n) is chosen inside the triangle so that the three small triangles ABD, ACD and BCD all have equal areas. What is the value of 10m+n?