SOLUTION: Adam is half as old as Bob and three times as old as Cindy. If the sum of their ages is 40, what is Bob's age? I know that the answer is 24 through a technique called "Backsolving

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Question 6199: Adam is half as old as Bob and three times as old as Cindy. If the sum of their ages is 40, what is Bob's age?
I know that the answer is 24 through a technique called "Backsolving". But I would like to know how to translate the problem into an equation or equations that can be used to solve the problem.
I got only this far:
Let x=Bob
Let y=Adam
Let z=Cindy
x+y+z=40
But after this I am confused about how to translate the the y and z variables into an equation format to get the correct solution.
Answer by jst_kidding(6) About Me  (Show Source):
You can put this solution on YOUR website!
easy sum !!
let the ages of-
bob=x
adam=x/2 (since he is half as old as bob)
cindys=x/6 (since adam is three times older than her)
Now-
x+ x/2 + x/6 = 40
LCM=6
By solving for x we get-
6x+3x+x=40*6
10x=40*6
x=24