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?

sugabreaddoughman Jul 13, 2024

#1**0 **

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.**

Maxematics Jul 13, 2024