SOLUTION: You have already invested $600 in a stock with an annual return of 11%. How much of an additional $1,500 should be invested at 12% and how much at 6% so that the total return on th

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Question 1089044: You have already invested $600 in a stock with an annual return of 11%. How much of an additional $1,500 should be invested at 12% and how much at 6% so that the total return on the entire $2,100 is 9%? (Round each answer to the nearest cent.)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
600 * .11 = 66

2100 * .09 = 189

189 minus 66 = 123

x = amount invested at 12%
y = amount invested at 6%

x + y = 1500
.12x + .06y = 123

solve for x in the first equation to get x = 1500 - y

replace x in the second equation to get .12 * (1500 - y) + .06y = 123

simplify to get 180 - .12y + .06y = 123

combine like terms to get 180 - .06y = 123

solve for y to get y = (180 - 123) / .06 = 950

since x + y = 1500, then x = 550

you have:

600 at 11% returns 66
550 at 12% returns 66
950 at 6% returns 57

total investment is 2100

total return is 189

189 / 2100 = 9%

everything checks out.

550 is invested at 12%
950 is invested at 6%