Posted by **Mary** on Friday, November 28, 2008 at 5:51am.

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 -
**Reiny**, Friday, November 28, 2008 at 11:23am
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 -
**drwls**, Friday, November 28, 2008 at 11:33am
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 -
**benny**, Tuesday, July 3, 2012 at 5:49pm
simply just wat is says above 168

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