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# Thank you so much

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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?

Aug 5, 2023

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Starting off

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

Aug 5, 2023