geometry
posted by neil .
A 30lb child is siting at A(2,3) and a 50lb child is at B(12,7) where units are feet .Find the point P between A and B which could be used as the fulcrum of a teeter board putting the two children in equilibrium.
30 AP=50 PB or (AP/PB)=5/3

A(2,3), P(x,y), B(12,7).
30AP = 50BP,
AP = (5/3)BP,
x  2 = 5/3(12x),
Multiply both sides by 3:
3x  6 = 5(12x),
3x  6 = 60  5x,
3x + 5x = 60 + 6,
8x = 66,
X = 8 2/8 = 8 1/4.
y 3 = 5/3(7y),
Multiply both sides by 3:
3y  9 = 5(7y),
3y  9 = 35  5y,
3y + 5y = 35 + 9 ,
8y = 44,
Y = 5 4/8 = 5 1/2.
Solution set: P(8 1/4,5 1/2).