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Question 992522: Pls I need help to solve the below case:
a man divides USD 10000 among 3 investors at 4%, 5%, 6% per year, respectively. its total income is USD 515 per year. his income from the 5% and 6% investments exceeds the income at 4% by USD 415. find how much is invested at each rate
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = investment at 4%
y = investment at 5%
z = investment at 6%
you have:
x + y + z = 10,000
.04x + .05y + .06z = 515
you are given that the investments at 5% and 6% exceed the investment at 4% by 415.
this means that .05y + .06z = .04x + 415
in the equation of .04x + .05y + .06z = 515, you can replace .05y + .06z with .04x + 415 because they are equivalent.
you will get:
.04x + .04x + 415 = 515
subtract 415 from both sides of this equation to get:
.08x = 100
divide both sides of this equation by .08 to get:
x = 1250.
if x = 1250, then .04x must be equal to 50.
the equation of .04x + .05y + .06z = 515 = 515 becomes:
50 + .05y + .06z = 515
subtract 50 from both sides of this equaton to get:
.05y + .06z = 465.
likewise, the equation of x + y + z = 10,000 becomes:
1250 + y + z = 10,000
subtract 1250 from both sides of this equation to get:
y + z = 8750.
you have two equations in two unknowns that you need to continue to solve.
they are:
y + z = 8750
.05y + .06z = 465
multiply both sides of the second equation by 20 and your equations becomes:
y + z = 8750
y + 1.2z = 9300
subtract the first of these equations from the second to get:
.2z = 550
divide both sides of this equation by .2 to get:
z = 2750
.06z = .06 * 2750 = 165
you now have:
x = 1250
z = 2750
.04x = 50
.06z = 165
since x + y + z must be equal to 10,000, and since x = 1250 and z = 2750, then y must be equal to 6000 because 1250 + 6000 + 2750 = 10,000.
since .04x + .05y + .06z must be equal to 515, and since .04x = 50 and .06z = 165, then .05y must be equal to 300 because 50 + 300 + 165 = 515.
looks like your problem is solved.
x = 1250
y = 6000
z = 2750
total = 10,000
.04x = 50
.05y = 300
.06z = 165
total = 515
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