Al, Betty, and Clare split $\$1000$ among them to be invested in different ways. Each begins with a different amount. At the end of one year they have a total of $\$1500$. Betty and Clare have both doubled their money, whereas Al has managed to lose $\$100$. What was Al's original portion?
a b and 1000-a-b are the amounts
2a + 2b + (1000-a-b -100) = 1500
a + b + 900 = 1500
a + b = 600
1000 - (a+b) = 400 is what Al had