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SOLUTION: George invested some money at 5% interest. George also invested $219 more than 4 times that amount at 10%. How much is invested at each rate if George receives $922.80 in interest

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adelekeademolu

Answer:

$1564 was invested at 5%

$6475 was invested at 10%

Step-by-step explanation:

Let the amount invested at 5% be X

And that invested at 10% be Y.

Interest on X

[tex]I_X=X \times5\%=0.05X[/tex]

Interest on Y

[tex]I_Y=Y \times10\%=0.1Y[/tex]

From the question,

[tex]Y=4X+219[/tex]

Interest on Y

[tex]I_Y=0.1(4X+219)=0.4IX+21.9[/tex]

Also, from the question, both interests add up to $922.80

[tex]I_X + I_Y = 922.8[/tex]

[tex]0.05X + 0.4X+21.9 = 922.8[/tex]

[tex]0.45X = 922.8- 21.9= 703.8[/tex]

[tex]X=\dfrac{703.8}{0.45}=1564[/tex]

[tex]Y = 4X+219=4\times1564+219[/tex]

[tex]Y=6256+219=6475[/tex]

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