Question
I had a total of 129 marbles in 3 boxes at first. then I threw away 2/3 of the marbles from box1 ,added 15 marbles to box 2 and added some marbles to box 3 until the number of marbles in box 3 tripled. As a result, the ratio of the number of marbles in box 1 to the number of marbles in box 2 to the number of marbles in box 3 became 2:3:9. what is the total number of marbles in the three boxes now?
Answers
oobleck
suppose the boxes 1,2,3 had x,y,z marbles, respectively.
Now, what has happened?
after step 1, we have x/3, y+15, 3z marbles in the boxes
At that point,
x/3 : y+15 : 3z = 2:3:9
So now you have to solve
3(x/3) = 2(y+15)
9(y+15) = 3(3z)
x+y+z = 129
-------------------
x = 72, y=21, z = 36
So the number of marbles has become
72/3 + 21+15 + 108 = 168
Now, what has happened?
after step 1, we have x/3, y+15, 3z marbles in the boxes
At that point,
x/3 : y+15 : 3z = 2:3:9
So now you have to solve
3(x/3) = 2(y+15)
9(y+15) = 3(3z)
x+y+z = 129
-------------------
x = 72, y=21, z = 36
So the number of marbles has become
72/3 + 21+15 + 108 = 168