SOLUTION: I am having a problem with an interest problem mainly because it has 3 unknowns. I can't seem to get the equations right. Can you help me? A man divides $10000 among 3 investmen

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Question 144949: I am having a problem with an interest problem mainly because it has 3 unknowns. I can't seem to get the equations right. Can you help me?
A man divides $10000 among 3 investments, 3%, 4% and 6% per annum respectively. His annual income from the first two investments is $80 less than his income from the third investment and his total income is $460 per year. Find the amount invested at each rate.
The answer is: 3% $3000; 4% $2500; 6% $4500
Thank you for your time.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x="amount @ 3%", y="amount @ 4%", and z="amount @ 6%"

"A man divides $10000 among 3 investments" __ x+y+z=10000

"His annual income from the first two investments is $80 less than his income from the third investment"
__ (3%)x+(4%)y=(6%)z-80

"his total income is $460 per year" __ (3%)x+(4%)y+(6%)z=460

substituting __ [(6%)z-80]+(6%)z=460 __ adding 80 __ (12%)z=540 __ dividing by 12% __ z=4500

substituting __ x+y+(4500)=10000 __ subtracting 4500 __ x+y=5500 __ subtracting x __ y=5500-x

substituting __ (3%)x+(4%)y=(6%)(4500)-80 __ (3%)x+(4%)y=190 __ dividing by 4% __ .75x+y=4750

substituting __ .75x+(5500-x)=4750 __ subrtacting 5500 __ -.25x=-750 __ dividing by -.25 __ x=3000

substituting __ (3000)+y=5500 __ subtracting 3000 __ y=2500