Question

Solve
Q.2. On a certain date, Jerry invested $ 10,000 at 3 percent simple annual interest rate and a different amount at 10 percent simple annual interest rate. What was the amount, in dollars, Jerry invested at interest rate of 10 percent if the total interest earned by Jerry's two investments in one year was $ 900?

Answer 1

Dear student

$$\begin{gathered} \mathrm{Here},{\mathrm{P}}_1=\&10,000 \\ {\mathrm{R}}_1=3\% \\ {\mathrm{T}}_1=1\mathrm{year} \\ \mathrm{So},{\mathrm{I}}_1=\frac{{\mathrm{P}}_1{\mathrm{R}}_1{\mathrm{T}}_1}{100}=\frac{10,000\times 3\times 1}{100}=\&300 \\ \mathrm{Also},{\mathrm{R}}_2=10\% \\ {\mathrm{T}}_2=1\mathrm{year} \\ \mathrm{and}\mathrm{Total}\mathrm{interest}\mathrm{earned}\mathrm{on}\mathrm{two}\mathrm{different}\mathrm{investments},\mathrm{I}={\mathrm{I}}_1+{\mathrm{I}}_2 \\ \Rightarrow 900=300+{\mathrm{I}}_2 \\ \Rightarrow {\mathrm{I}}_2=\&600 \\ \Rightarrow \frac{{\mathrm{P}}_2{\mathrm{R}}_2{\mathrm{T}}_2}{100}=600 \\ \Rightarrow \frac{{\mathrm{P}}_2\times 10\times 1}{100}=600 \\ \Rightarrow \boxed{{\mathbf{P}}_{\mathbf{2}}\mathbf{=}\mathbf{\&}\mathbf{6000}} \\ \mathrm{So},\mathrm{Jerry}\mathrm{invested}\&6000\mathrm{at}\mathrm{interest}\mathrm{rate}\mathrm{of}10\mathrm{percent}. \end{gathered}$$
Regards