Math

mr. and mrs. garcia have a total of 100000$ to be invested in stocks, bonds, and a money market account. the stocks have a rate of return of 12% per year, while the bonds and the money market account pays 8% per year and 4% per year, respectively. the garcias have stipulated that the amount invested in the money market account should be equal to the sum of 20% of the amount invested in stocks and 10% of the amount invested in bonds. how should the garcias allocate their resources if they require an annual income of 10000$ from their investments ?

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  1. amount invested in stocks ---- s
    amount invested in bonds ---- b
    amount invested in money market = .2s + .1b

    s + b + .2s + .1b = 100,000
    12s + 11b = 1,000,000 **

    .12s + .08b + .04(.2s+.1b) = 10,000
    .128s + .084b = 10,000
    128s + 84b = 10,000,000
    32s + 21b = 2,500,000 ***

    solve ** and *** using your favourite method, it comes out nicely

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