Question

linda $200,000 in a state lottery. She first paid income tax of 30% on thewinnings. Of the rest she invested some at 1.5% and some at 4%, earning $4250interest per year. How much did she invest at each rate?

Answer 1

Given:

Total money win is $200,000.

`\begin{gathered} B\text{alance amount after the tax paid=200,000}*(70)/(100) \\ B\text{alance amount after the tax paid=}140,000 \end{gathered}`

Let the amount invested at 1.5% be x

`\begin{gathered} (x*(1.5)/(100))+(\lbrack140,000-x\rbrack*(4)/(100))=4250 \\ (1.5x+560,000-4x)/(100)=4250 \\ -2.5x+560,000=425,000 \\ -2.5x=425,000-560,000 \\ -2.5x=-135,000 \\ 2.5x=135,000 \\ x=(135,000)/(2.5) \\ x=54000 \end{gathered}`
`\text{Amount invested in 1.5\% =\$54000}`
`\begin{gathered} \text{Amount invested in 4\%=140,000-54000} \\ \text{Amount invested in 4\%}=\text{ \$}86000 \end{gathered}`