+145 Mike had 56 more trading cards than Aron. During a game, Mike lost 2/5 of his cards to Aron. Now, Aron has 72 more cards than Mike. How many cards did each of them have at first?
+106 Let's call m the number of cards Mike has and a the number of cards Aaron has. We can write the following equations:
\(m = a+56\)
\(a = \frac{3}{5}m+72\)
Let's use elimination to solve this
\(5a = 3m + 360\)
\(-3a=-3m+168\)
\(2a=528\)
\(a=264\)
\(m = (264)+56\)
\(m = 320\)
Let's double-check our answers:
\((320)= (264)+56\)
\(320=320\)
\((264) = \frac{3}{5}(320)+72\)
\(264=192+72\)
\(264=264\)
So both numbers are correct. Therefore, Mike has 264 cards and Aaron has 320 cards.
