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A total of $27,000 is invested, part of it at 12% and the rest at 13%. The total interest after one year is $3385. How much was invested at each rate?

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The amount invested in each rate are $14500 and $12500 respectively;

Let the amount invested in each be P1 and P2

Let the individual interest be I1 and I2 respectively;

I1 = P1R1T/100

I2 = P2R2T/100

If a total of $27,000 is invested, then;

P1 + P2 = 27000 ........... 1

If the total interest after one year is $3385, then;

I1 + I2 = 3385

[tex]\frac{P_1(12)(1)}{100} + \frac{P_2(13)(1)}{100} = 3385\\0.12P_1+0.13P2=3385\\12P_1 + 13P_2=338500 ........................... 2[/tex]

Solving equations 1 and 2 simultaneously;

P1 + P2 = 27000 ........... 1 * 12

12P1 + 13P2 = 338500 ........... 2 * 1

________________________________

12P1 + 12P12 = 324000

12P1 + 13P2 = 338500 ...

Subtract both equations

12P2 - 13 P2 = 324000 - 338500

-P2 = -14500

P2 = 14500

Recall that P1 + P2 = 27000

P1 = 27000 - P2

P1 = 27000 - 14500

P1 = 12500

Hence the amount invested in each rate are $14500 and $12500 respectively;

Learn more here: https://brainly.com/question/19088526

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