Question

An actor invests some money at 5%, and $38000 more than twice the amount at 9%. The total annual interest earned from the investment is $37460 How much did he invest at each amount? Use the sle-step method.CEHe invested at 5% and $at9%

Answer 1

Let the amount invested at 5% be

`=x`

interest earned will be

`(5)/(100)* x=0.05x`

38,000 more than twice the amount at 9% will be

`\begin{gathered} (9)/(100)(2x+38,000) \\ 0.09(2x+38,000) \end{gathered}`

The total amou nt amount invested will be represented below as

`\begin{gathered} 0.05x+0.09(2x+38,000)=37460 \\ 0.05x+0.18x+3420=37460 \end{gathered}`

By simplifying further, we will have

`\begin{gathered} 0.05x+0.18x+3,420=37,460 \\ 0.23x=37460-3420 \\ 0.23x=34040 \\ x=(34040)/(0.23) \\ x=148,000 \end{gathered}`
`\begin{gathered} 2x+38000 \\ 2(148000)+38000 \\ 296000+38000 \\ =334000 \end{gathered}`

Hence,

The actor invested $148,000 at 5%

The actor invested $334,000 at 9%