There were 75 rocks is Boxes A,B, and C. After moving 28 rocks fro Box A to B, 24 rocks from B to C, and 19 rocks from C to A,there was an equal number of rocks in each box. How many rocks were in Box A in the beginning?

Question

30-04-2014
Mathematics

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There were 75 rocks is Boxes A,B, and C. After moving 28 rocks fro Box A to B, 24 rocks from B to C, and 19 rocks from C to A,there was an equal number of rocks in each box. How many rocks were in Box A in the beginning?

Answer :

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Cam943 Cam943 · Answer 1 · 2014-04-30T23:01:48-04:00

I actually did this kind of question earlier today in a math contest. It took me a while to get it, but it was quite easy.

So we basically know that:

[tex]A+B+C=75[/tex]

Now here comes the tricky part. We have to determine how many rocks there are in each box.

The easy thing about this is that we already know what will be in the boxes after the movements. It's just [tex]75÷3[/tex].

So now we know, that after the movements, each of the boxes will contain 12.

Lets do the operations on the boxes.

[tex]A-28+19=25[/tex]
[tex]B-24+28=25[/tex]
[tex]C-19+24=25[/tex]

And we find that:

[tex]A=34[/tex]
[tex]B=21[/tex]
[tex]C=20[/tex]

And from that, we get:

[tex]A=34[/tex]

Hope that helped! Enjoy.

~Cam943, Junior Moderator