When brooklyn and kayla left for their trip, the ratio of brooklyn's money to kayla's money was 7: 3. after a short while brooklyn gave kayla $30, making the new ratio of their cash 3: 2. when they started the trip, how much more money did brooklyn have than kayla? open add class comment…

Initially, brooklyn has $120 more money than Kayla. Here's the calculation

Beginning ammount

B : K   = 7  : 3

Brooklyn original amount = 7x
Kayla original amount  = 3x

After brooklyn give the money : 

(B - 30) : (K + 30) =  3:2

(7x - 30) / (3x + 40)  = 3/2
  
2 (7x-30)  =  3(3x+30)
14x - 60  = 9x + 90
14x - 9x  = 90 + 60

5x = 150     ;  x = 30

So, original amount of Brooklyn and Kayla's money:

Brooklyn = 7x = 7 x 30 = 210
Kayla = 3x = 3x 30    = 90

The difference is 210 - 90 = 120