Elena receives ​$131 per year in simple interest from three investments totaling ​$3000. Part is invested at​ 3%, part at​ 4% and part at​ 5

Question

Elena receives ​$131 per year in simple interest from three investments totaling ​$3000. Part is invested at​ 3%, part at​ 4% and part at​ 5%. There is ​$1000 more invested at​ 5% than at​ 4%. Find the amount invested at each rate.
The amount invested at​ 3% is ​$___ the amount invested at​ 4% is ​$___ , and the amount invested at​ 5% is ​$___

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Thu Nguyệt 3 years 2021-08-19T04:27:39+00:00 1 Answers 4 views 0

Answers ( )

  1. bonexptip
    0
    2021-08-19T04:29:18+00:00
    Reply

    Answer:

    600 at 3%

    700 at 4%

    1700 at 5%

    Step-by-step explanation:

    let x= amount invested at 3%

    y= amount invested at 4%

    z= amount invested at 5%

    equation 1: x+y+z= 3000

    Equation 2: .03x+.04y+.05z= 131

    Equation 3: z=y+1000

    Substitute equation 3 into equation 1

    x+y+(y+1000)= 3000

    x+2y=2000 (equation 4)

    Substitute equation 3 into equation 2

    .03x+.04y+.05(y+1000)=131

    .03x+.04y+.05y+50=131

    .03x+.09y= 81 (equation 5)

    Mulitply equation 4 by .03

    .03x+.06y=60

    Subtract this from equation 5

    (.03x+.09y)-(.03x+.06y)=81-60

    .03y=21

    y=700

    Plug y=700 into equation 4

    x+2(700)=2000

    x= 600

    Plug x= 600 and y=700 into equation 1

    600+700+z=3000

    z= 1700

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