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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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Mathematics
3 years
2021-08-19T04:27:39+00:00
2021-08-19T04:27:39+00:00 1 Answers
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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