# SOLUTION: \$10,000 is to be invested in three different ways. One part of the money is used to purchase mutual fund that offer a return of 8% per year. The second part, which amounts to twice

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 Question 607390: \$10,000 is to be invested in three different ways. One part of the money is used to purchase mutual fund that offer a return of 8% per year. The second part, which amounts to twice the first, is used to buy government bonds at 9% per year. The remainder is put in the bank at 5% annual interest. In the first year, the investments bring a return of \$830. How much was invested in each way? This is a matrices problem but I am confused with how to begin with the equations. Is one equation x + y + z = 10,000? The second equation.. Is is something like this? 0.08x + 2(0.09)y = I will be able to solve the problem after understanding how to put the wording into equations.. I understand how to solve matrices, so I am not asking for help with that. Thank you.Answer by ankor@dixie-net.com(15656)   (Show Source): You can put this solution on YOUR website!\$10,000 is to be invested in three different ways. One part of the money is used to purchase mutual fund that offer a return of 8% per year. The second part, which amounts to twice the first, is used to buy government bonds at 9% per year. The remainder is put in the bank at 5% annual interest. In the first year, the investments bring a return of \$830. How much was invested in each way? : Let x = amt invested at 8% Let y = amt invested at 9% Let z = amt invested at 5% : "\$10,000 is to be invested in three different ways." x + y + z = 10000 : "One part of the money is used to purchase mutual fund that offer a return of 8% per year. The second part, which amounts to twice the first, is used to buy government bonds at 9% per year." y = 2x -2x + y = 0 : " the first year, the investments bring a return of \$830. .08x + .09y + .05z = 830 : From these three equations we can derive a matrix 1, 1, 1, 10000 -2, 1, 0, 0 .08, .09, .05, 830 How much was invested in each way?