You are attempting to build a portfolio using the index model, and are currently trying to decide how much of your risky portfolio you want in the actively managed portfolio, and how much you want in the index fund. You have previously computed that, assuming the beta of your actively managed portfolio is 1, you should put 52% of your money in the active portfolio, and the rest in the index fund. If the beta of your actively managed portfolio is actually 0.8, what percent of your money should you put in the active portfolio?

-The answer is 0.471

How do you get this value? Please show all work.