Respuesta :
The annual interest is determined using the following formula:
[tex]A=P\times i\times t[/tex]Where "A" is the interest, "i" the interest rate in decimal notation and "t" represents time. "P" is the amount invested:
Since the combined interest is $570:
[tex]P_P\times i_P\times t_{}+P_M\times i_M\times t=570[/tex]And since the combined investment was $6000 we have:
[tex]P_P+P_M=6000[/tex]Solving for the amount invested by Martha:
[tex]P_P=6000-P_M[/tex]replacing in the formula for the interest:
[tex](6000-P_M)\times i_P\times t_{}+P_M\times i_M\times t=570[/tex]Replacing the known values:
[tex](6000-P_M)\times(0.06)\times t_{}+P_M\times(0.12)\times t=570[/tex]Simplifying:
[tex]360t-0.06P_Mt+0.12P_Mt=570[/tex]Now we solve for the amount invested by Martha:
[tex]\begin{gathered} -\text{0}.06P_Mt+0.12P_Mt=570-360t \\ P_M(-0.06t+0.12t)=570-360t \\ P_M=\frac{570-360t}{-0.06t+0.12t} \end{gathered}[/tex]Since we are not given the amount of time "t", we can't determine the exact value of the amount invested by Martha.
