Andy and Brian each had a collection of picture cards at first. Andy gave 3/4 of his picture cards to Brian. Brian then gave 80% of his picture cards back to Andy. In the end, Andy had 297 picture cards and Brian had 63 picture cards. How many picture cards does each boy have at first?

Answer 1

Andy =A
(1/4)A + 0.80( B+ 3/4 A) = 297
0.25 A + 0.80 B + 0.60 A = 297
0.85 A + 0.80 B = 297 first equation

Brian = B
(B + 3/4 A) - 0.80(B + 3/4 A) = 63
0.20 ( B + 0.75 A) = 63
B + 0.75 A = 315 second equation

Answer 2

0.25A = 297 - 252
0.25A/0.25 = 45/0.25
A = 180
B = 315 - 0.75(80)
B = 180