After the 1st exchange:
Zach will have 5/7 of his initial cookies
Trina will have 2/7 of Zach's initial cookies and 1/1 of her own initial cookies

After the 2nd exchange:
Zach will have 5/7 of his initial cookies + 3/5 of trina's cookies after the 1st exchange ,[2/7 Zach's initial and 1/1 of Trina's initial] =360

Trina will have 2/5 of her cookies after the first exchange,which is 2/5 of (2/7 zach's initial and 1/1 of her initial cookies at first) =60

We can work backwards to find Trina's cookies after the 1st exchange=60/2 x 5=150

Then, we can find 3/5 of 2/7 of zach's initial cookies and trina's initial cookies,aka the cookies trina gave to zach in the 2nd exchange:

60/2 x 3 =90

Now, we can fins 5/7 of zach's initial cookies=360-90=270
And finally, the number of cookies zach had at first =270/5 x 7=378

hope this helps your homework