A Problem of Drinks

              I love to mix drinks. When I have one glass orangeade and one glass lemonade each glass contains the same amount. I take 2 ounces full of the orangeade and mix it with the lemonade, and then I take 2 ounces full of this mixture and put it back in the orangeade. What do you think of the resulting mixture?

             Do you think there is more orangeade in the lemonade or more lemonade in the orangeade?

Answer:  Neither. There is same amount in each. Let us assume:

A= amount of orangeade in glass at start

B= amount of orangeade first transferred.

      C= amount of orangeade transferred second time

D= amount of Lemonade transferred to orangeade

Now we must show that the amount of Lemonade in orangeade equals the amount of orangeade in the Lemonade or, in terms of a ,b, c, d we must show that:

D= b –c

 Time                                                Amount of Orangeade in Glass

Start                                                                      a

1^st Transfer                                                         a – b

2^nd Transfer                                                (a-b) + (c + d)

The starting amount, a, must equal the final amount after the second transfer.

A= (a-b) + c +c d or d = b - c