SOLUTION: You have already invested $550 in a stock with an annual return of 11%. How much of an additional $1,600 should be invested at 12% and how much at 6% so that the total return on th

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Question 911728: You have already invested $550 in a stock with an annual return of 11%. How much of an additional $1,600 should be invested at 12% and how much at 6% so that the total return on the entire $2,150 is 9%? (Round each answer to the nearest cent.)
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
z+x+y=2150
.11*550+0.06*x+0.012*y=.09*2150
60.50+0.06*x+0.012*y=193.50
2150-550=1600
193.50-60.50=133
Now we have two equations in two unknowns
x+y=1600
0.06*x+0.012*y=133
Total amount of money invested: $1600
x+y=1600,
Total yearly interest for the two accounts is: $133
0.06*x+0.12*y=133
x=1600-y
Substitute for x
0.06*(1600-y)+0.12*y=133
Multiply out
96-0.06*y+0.12*y=133
Combine like terms.
0.06*y=37
Isolate y
y=$ 616.67 at 12% earns $74.00 interest
x=1600-y
Calculate x
x=$ 983.33 at 6% earns $59.00 interest
Check
0.06*983.333333+0.12*616.666667=133
59.0+74.0=133
133.0=133
If this statement is TRUE and neither x nor y is negative then all is well
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