An actor invested some money at 5% simple interest, & $41,000 more than four times the amount at 9%. The total amount interest earned from the investment was $35,260. How much did he invest at each amount?

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calculista calculista · Answer 1 · 2020-04-13T07:50:52+02:00

Answer:

An actor invested $77,000 at 5% and invested $349,000 at 9%

Step-by-step explanation:

Let

x ----> the amount invested at 5%

(4x+41,000) ----> the amount invested at 9%

we know that

The interest earned by the amount invested at 5% plus the interest earned by the amount earned at 9% must be equal to $35,260

so

The linear equation that represent this situation is

[tex]0.05x+0.09(4x+41,000)=35,260[/tex]

solve for x

[tex]0.05x+0.36x+3,690=35,260[/tex]

[tex]0.41x=35,260-3,690\\0.41x=31,570\\x=\$77,000[/tex]

[tex](4x+41,000)=4(77,000)+41,000=\$349,000[/tex]

therefore

An actor invested $77,000 at 5% and invested $349,000 at 9%