Ratio
posted by Mary on .
I had a total of 129 marbles in 3 boxes at first. Then I threw away 2/3 of the marbles from Box 1, added 15 marbles to Box 2, and added marbles to Box 3 until the numbers in box 3 tripled. As a result the number of marbles in box 1 to the number in Box 2 to the number of marbles in box 3 became 2:3:9 Wat is the total number of marbles in the 3 boxes?

let the number of marbles be as follows:
Box1 x
Box3 y
Box2 129xy
after the described action
box1 = x/3 (you took 2/3 away, so 1/3 remains)
box2 = 129xy + 15 = 144xy
box3 = 3y
then (x/3) : 144xy : 3y = 2:3:9
so then (x/3)/(144xy) = 2/3
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3x + 2y = 288 (equ#1)
also (x/3)/3y = 2/9
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x = 2y (equ#2) sub that into equ#1 to get
y = 36
then x = 72
check:
original
box1 72
box2 21
box3 36  total 129
after action:
box1 = 24
box2 = 36
box3 = 108
24:36:108 = 2:3:9 
After: 24:36:108 (total 168)
Before: 72:21:36 (total 129)
Method used: trial and error
Start with "after" combinations with the right ratios, determine the required operations and "before" compositions, and see which one adds up to 129 "after".
It only took three attempts. 
simply just wat is says above 168