Alan invests a total of 12500 in three different ways He in

Alan invests a total of $ 12,500 in three different ways. He invests one part in a mutual fund which in the first year has a return of 11%. He invests the second part in a government bond at 7% per year. The third part he puts in the bank at 5% per year. He invests twice as much in the mutual fund as in the bank. The first year Alan\'s investments bring a total return of $ 965. How much did he invest in each way?

Solution

Let B = amount he invests in the bank and G = the amount he invests in a government bond. Then we know that the amount he invests in the mutual fund = 2B, right? So the first thing we can say is

2B + G + B = 15000, or

(1) 3B + G = 15000

Also, the sum of his returns in the first year is

.11(2B) + .07G + .05B = 1170, or .22B + .07G + .05B = 1170, which yields

(2) .27B + .07G = 1170

From (1) we get that G = 15000-3B, so we substitute in (2) and solve

.27B + .07(15000 - 3B) = 1170