word problem

Question

Isiah and andy had a total of 560 trading cards . After Isiah gave 1/9 of his trading cards to Andy they had an equal number of trading cards. How many more trading cards did Isiah have than Andy in the beginning?

Answer 1

Let x = number of cards for Isiah initially

     y = number of cards for Andy initially

 

Then, x + y = 560

        x - (1/9)x = y + (1/9)x

 

So, after multiplying the second equation by 9, we arrive at

9x - x = 9y + x, so 7x = 9y, or equivalently, 7x - 9y = 0

 

We now have the system:  x + y = 560

                                     7x - 9y = 0

 

Multiply the first equation by -7 to obtain:  -7x - 7y = -3920

                                                             7x - 9y = 0

 

Adding the equations, we get -16y = -3920

 

So, y = 245 and x = 560 - 245 = 315.

 

ANSWER:  Isiah had 315 cards and Andy had 245 cards at the beginning.