Perry had 72 more game cards than Dave. Perry gave 1/3 of his game cards to Dave. Dave gave 3/8 of his game cards to Perry in return. In the end, Perry had 114 game cards more than Dave. How many game cards did Perry have at first?

Guest Aug 5, 2023

#1**+1 **

Starting off

Dave had D game cards

Perry had D + 72

Perry gave (1/3) of his cards to Dave

Dave now has (1/3)(D + 72) + D = (4/3)D + 24

Perry now has (2/3) (D + 72) = (2/3)D + 48

Dave then gave 3/8 of his cards to Perry

Dave now has (5/8) [ (4/3)D +24 ] = (5/6)D + 15

Perry now has (2/3)D + 48 + (3/8)[(4/3)D + 24] = (2/3)D + (1/2)D + 48 +9 = (7/6)D + 57

And the difference at the end was that Perry had 114 more cards than Dave

So

Perry's - Dave's = 114 in equation form we have

[ (7/6)D + 57] - [ (5/6)D + 15 ] = 114 simplify

(2/6)D + 57 -15 = 114

(1/3)D + 42 = 114

(1/3)D = 114 - 42

(1/3)D = 72 multiply through by 3

D = 216 = what Dave started with

D + 72 = 216 + 72 = 288 = what Perry started with

CPhill Aug 5, 2023