The rate of simple interest for the first investment, R1=4%.
The rate of simple interest for the second investment, R2=11%.
The total interest for both investments, SI= $142.40.
Let P1 be the amount invested in the first investment and P2 be the amount invested in the second investment.
Since the second investment had $340.00 more money than the first,
we can write
[tex]P2=P1+340[/tex]Now, the total interest for both investments can be expressed as,
[tex]SI=\frac{R1}{100}\times P1+\frac{R2}{100}\times P2[/tex]Put the avlues in the above equation.
[tex]\begin{gathered} 142.4=\frac{4}{100}\times P1+\frac{11}{100}\times(P1+340) \\ 142.4\times100=4P1+11\times(P1+340) \\ 14240=4P1+11P1+11\times340 \\ 14240=15P1+3740_{} \\ 15P1=14240-3740 \\ 15P1=10500 \\ P1=\frac{10500}{15} \\ P1=700 \end{gathered}[/tex]Now, P2 can be found as,
[tex]\begin{gathered} P2=P1+340 \\ =700+340 \\ =1040 \end{gathered}[/tex]Therefore, the amount invested in the first investment is $700 and the amount invested in the second investment is $1040.
