|
Question 161626: please help me .A person invested $10,000. the greater part is invested at 6% and the remainder at 5%. The annual income from the greater part is $160 more then the annual income from the smaller part. What is the smaller part of the investment? Thank you very much for your help.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! total amount invested is 10000
let x = greater part
let y = smaller part
-----
investment equation is
x + y = 10000
-----
greater part is invested at 6%
smaller part is invested at 5%
-----
total income equation is
.06*x + .05*y = total income
-----
income from greater part is $160 more than annual income from smaller part.
-----
income equation becomes
.06*x = .05*y + 160
subtracting .05*y from both sides and it becomes
.06*x - .05*y = 160
-----
can't think of anything else to be in there.
you have two equations to work with.
first is investment equation.
next is income equation after it was modified to show how much more income from greater part (x) than smaller part (y).
those are
-----
x + y = 10000
.06*x - .05*y = 160
-----
multiply second equation by 100 to get rid of the decimals.
equations become
x+y = 10000
6*x - 5*y = 16000
-----
multiply first equation by 6 so we can eliminate one of the unknowns.
equations become
6*x + 6*y = 60000
6*x - 5*y = 16000
-----
subtract second equation from first.
6*x + 6*y = 60000
- 6*x - 5*y = 16000
-----------------
= 0*x + 11*y = 44000
-----
x has been eliminated and remaining equation to work with is
11*y = 44000
y = 4000
-----
that's the smaller part of the investment.
to get the greater part of the investment, substitute in the investment equation
x + y = 10000
x + 4000 = 10000
x = 6000
-----
that's the greater part of the investment
-----
to prove this answer is correct, calculate the interest from each part of the investment.
.06*(6000) = 360 = income from greater part of the investment (x).
.05*(4000) = 200 = income from smaller part of the investment (y).
360 - 200 = 160 = amount of income from x greater than amount of income from y.
-----
greater part of the investment = 6000
smaller part of the investment = 4000
is your answer.
|
|
|
| |
