Let x be her total investment. Then:
Rate 1: 6% = 0.06
Rate 2: 12% = 0.12
Total interest = $720
[tex]0.06(0.5x)+0.12(0.5x)=720[/tex]
Simplify:
[tex]\begin{gathered} 0.03x+0.06x=720 \\ 0.09x=720 \end{gathered}[/tex]
Solve for x:
[tex]\begin{gathered} \frac{0.09x}{0.09}=\frac{720}{0.09} \\ x=8000 \end{gathered}[/tex]
Next, the investment in each be is:
[tex]\begin{gathered} First:\text{ 0.06\lparen0.5\rparen\lparen8000\rparen=240} \\ Second:0.12(0.5)(8000)=480 \end{gathered}[/tex]
Answer:
Investment for each: $240 and $480 for the other half
Total investment: $8000
