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 ​$___ , and the amount invested at​ 5% is ​$___

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