Problem #1063


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?

$\textbf{(A) }$$250 \qquad\textbf{(B) }$ $350 \qquad\textbf{(C) }$$400\qquad\textbf{(D) }$ $450\qquad\textbf{(E) }$$500$

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Instructions for entering answers:

  • Reduce fractions to lowest terms and enter in the form 7/9.
  • Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
  • Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
  • Exponents should be entered in the form 10^10.
  • If the problem is multiple choice, enter the appropriate (capital) letter.
  • Enter points with parentheses, like so: (4,5)
  • Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i).

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