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Santiago receives ​$133 per year in simple interest from three investments. Part is invested at​ 2%, part at​ 3%, and part at​ 4%. There is​ $500 more invested at​ 3% than at​ 2%. The amount invested at​ 4% is two times the amount invested at​ 3%. Find the amount invested at each rate. the amount invests at 2% is how much $?

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I first found variables to let the amount invested be at. Then have the variables I choose represent y and z. The amount invested at 2% = $600. The amount invested at 3% = $1,100. The amount invested at 4% = $2,200. Total amount invests at 2% = $600 :)
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