The points L, M, N and O all lie on the same line segment, in that order, such that the ratio of LM:MN:NOLM:MN:NO is equal to 6:1:2.6:1:2. If LO=45,LO=45, find MO.MO.

Answer 1

LM:MN:NO is equal to 6:1:2. This can be written as:

LM/6=MN/1=NO/2=k (since they all have the same ratio)

or

LM=6k

MN=k

NO=2k

Since LO=LM+MN+NO=45 we have 6k+k+2k=45

Solving for k we get k=5

So MO=MN+NO=5+2•5=15