easy math problem.. 10 points!?

Jeremy bought postcards on a trip. He sent 5 cards to his aunt. He sent half of the remaining cards to friends. Then he sent one of the remaining cards sister. He was left with 4 cards. Write an equation to find out how many postcards Jeremy bought

T = total #

T = 5 (to the aunt) + 1/2 (T - 5) (to his friends) + 1 (to his sister) + 4 (left)

T = 5 + 1/2 (T - 5) + 1 + 4

T = 10 + 1/2 (T - 5)

2T = 20 + (T - 5)

2T = 20 + T - 5

2T = 15 + T

T = 15

Check the original problem
-----
5 to aunt, (leaves 10)
1/2 remaining (5) to friends (leaves 5)
1 to sis (leaves 4)

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