Answer:
5:2
Explanation:
ON = OA + AN
AN = 2/5AB
AB = 5b-4a
AN = 2b - 8/5a
ON = 4a - 8/5a +2b
ON = 12/5a+2b
OP = k(12/5a+2b)
OP = OA + AP
AP = x(AM)
AM = 5/2b-4a
OP=4a-4ax+5/2bx
OP=4a-4ax+5/2bx and OP=12/5ak+2bk
Coefficients of A
4-4x=12/5k
k=(20-20x)/12
Coefficients of B
5/2x=2k
k=5/4x
(20-20x)/12 =5/4x
20=35x
x=4/7
k=5/4 * 4/7 = 5/7
OP=k(ON)
OP = 5/7
PN = 2/7
OP:PN = 5:2
I figured it out after posting the question, typing from a different account. I hope this helps somebody.