Answer: She invest 41500 at 7% interest and 900 at 11% interest.
Step-by-step explanation:
Formula for simple interest = [tex]\dfrac{\text{Principal x rate x Time}}{100}[/tex]
Let [tex]P_1=\$1500,\ P_2=\$900\ \ \ \ , r_1=r, \ \ r_2=r+4,\ \ \ t_1=t_2=1[/tex]
Simple interest by first investment = [tex]\dfrac{P_1r_1t_1}{100}=\dfrac{1500(r)(1)}{100}=15r[/tex]
Simple interest by second investment = [tex]\dfrac{P_2r_2t_2}{100}=\dfrac{900(r+4)(1)}{100}=9(r+4)[/tex]
As per given,
Total interest = $204
[tex]\Rightarrow 15r+9(r+4)=204\\\\\Rightarrow\ 15r+9r+36=204\\\\\Rightarrow\ 24r=204-36\\\\\Rightarrow\ 24r=168\\\\\Rightarrow\ r=\dfrac{168}{24}\\\\\Rightarrow\ r=7\%[/tex]
Hence, she invest 41500 at 7% interest and 900 at 11% interest.
