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George invested some money at 11% interest. George also invested $⁢159 more than 4 times that amount at 13%. How much is invested at each rate if George receives $⁢760.29 in interest after one year? (Round to two decimal places if necessary.)​

Sagot :

Sqdancefanidn

Answer:

 $1174 at 11%

  $4855 at 13%

Step-by-step explanation:

You want the amounts of George's investments if the total interest on the amount invested at 11% and 4 times that amount plus $159 invested at 13% came to $760.29 for the year.

Setup

Let x represent the amount invested at 11%. Then the amount invested at 13% is (4x+159). The total interest is ...

  0.11x + 0.13(4x +159) = 760.29

Solution

Simplifying the equation, we have ...

  0.11x +0.52x + 0.13·159 = 760.29

  0.63x = 760.29 -0.13·159

  x = (760.29 -0.13·159)/0.63 = 1174

The amount invested at 13% is then ...

  4(1174) +149 = 4855

George invested $1174 at 11% and $4855 at 13%.

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