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An investor has a £40,000 portfolio, 40% of which is invested in bonds.The investor wishes to add funds to the portfolio by purchasing bonds so that 52% of the entire portfolio is invested in bonds. What value of bonds should the investor purchase?

My solution is as follows:

40% of the portfolio is £16,000, and 52% of the portfolio is £20,800. Thus in order for the portfolio to be consist of 52% bonds, the investor must purchase £20,800 - £16,000 = £4,800 worth of bonds. Once the investor has spent an extra £4,800 on bonds, this brings the total amount spent on bonds to £20,800, which is 52% of the portfolio.

The actual answer is £10,000. How is my solution wrong and where am I misunderstanding?

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The portfolio is worth 40000, after adding to it it will be worth 40000+X. The portfolio now has 16000 in bonds, after adding it will have 16000+X in bonds. Find X such that (16000+X)/(40000+X) = 0.52

The answer is 10000.

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