# Ratio

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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?

• Ratio -

let the number of marbles be as follows:
Box1 x
Box3 y
Box2 129-x-y

after the described action

box1 = x/3 (you took 2/3 away, so 1/3 remains)
box2 = 129-x-y + 15 = 144-x-y
box3 = 3y

then (x/3) : 144-x-y : 3y = 2:3:9

so then (x/3)/(144-x-y) = 2/3
.
.
3x + 2y = 288 (equ#1)

also (x/3)/3y = 2/9
.
.
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

• Ratio -

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.

• Ratio -

simply just wat is says above 168

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