Question 57088
Let x = the additional amount to be invested at 14%

The interest on the initial $15,000 at 11% would be 0.11($15,000)
The interest on the additional amount, $x at 14% would be 0.14($x)
The sum of these two amounts of interest should come to 12% of ($15,000 + $x) or 0.12($15,000+$x).  So...putting it all together. you can write:

0.11($15000) + 0.14($x) = 0.12($15000+$x) Simplify this and solve for x.
$1650 + 0.14x = 1800 + 0.12x  Subtracting 0.12x from both sides, you get:
1650 + 0.02($x) = $1800  Subtract $1650 from both sides.
0.02($x) = $150  Finally, divide both sides by 0.02
x = $7500

So Helen Weller should invest an additional $7,500 at 14% interest to obtain an average rate of return of 12% on the entire amount.

Check: 

11% of $15,000 = 0.11($15,000) = $1,650
14% of $7,500 = 0.14($7,500) = $1,050
The sum: $1,650 + $1,050 = $2,700 total interest.

12% of ($15,000 + $7,500) = 0.12($22,500) = $2,700