SOLUTION: Point B belongs to AC so that AB:BC=2:1. Point D belongs to AB so that AD:DB=3:2. Find AD:DC?

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Question 1122811: Point B belongs to AC so that AB:BC=2:1. Point D belongs to AB so that AD:DB=3:2. Find AD:DC?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Point B belongs to AC so that AB:BC=2:1.
Point D belongs to AB so that AD:DB=3:2. Find AD:DC?
:
let x = the first multiplier
let y = the 2nd multiplier
A------------D-------B--------C
AB = 2x
BC = x
AC = 3x
:
AD = 3y
DB = 2y
AB = 5y
therefore
2x = 5y
x = 5%2F2y
x = 2.5y
;
Find AD:DC?
AD = 3y,
DC = 3x - 3y
replace x with 2.5y
DC = 3(2.5y-3y)
DC = 7.5y - 3y
DC = 4.5y
:
%28AD%29%2F%28DC%29 = %283y%29%2F%284.5Y%29 = 2:3 is AD:DC