Tray A had 132 more cookies than Tray B at first.

Now, 116 cookies are being transferred from Tray B to Tray A.

As a result, Tray B has 116 cookies less than before and Tray A has 116 cookies more than before. This is a total “swing” of 232 cookies, so now Tray A has 364 more cookies than Tray B.

But we know that Tray A has 3 times as many cookies as Tray B in the end.

So Tray A has 2 units more cookies than Tray B.

2 units = 364 cookies
1 unit = 182 cookies
3 units = 546 cookies

So Tray A has 546 cookies at the end.

Number of cookies on Tray A at first
= 546 - 116
= 430

If you have done the calculations, Tray B had 182 + 116 = 298 at first, for a difference of 132 cookies.

To understand this, let me illustrate an example.

Suppose you have $5 and I have $5.

I pass you $5. Now, how much more money do you have than me?

When I pass you my $5, I would have $5 less (for a final amount of $0) and you would have $5 more (for a final amount of $10).

So the difference is $10, even though I pass you $5 only. This is because there are two processes involved when I pass you $5. First, I lose the $5. Next, you gain the $5. If you draw the model diagram, you will realise that the model will go like this.

Before:

xxxxx
xxxxx

After:

xxxxxxxxxx
(blank)

Your side of the model gets lengthened by $5 and my side of the model gets shortened by $5.

Tnks!!!! :)