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Question 71027: Stan invested $5,000, part at 8% and part at 17%. If the total interest at the end of the year is $490, how much did he invest at 8%?
thank
Found 2 solutions by checkley75, bucky:
Answer by checkley75(3666)   (Show Source):
You can put this solution on YOUR website! .08x+.17(5000-x)=490
.08x+850-.17x=490
-.09x=490-850
-.09x=-360
x=-360/-.09
x=4000 invested @ 8%
proof
.08*4000+.17(5000-4000)=490
320+.17(1000)=490
320+170=490
490=490
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! We will need two equations to solve this problem. But first, recognize the fact that there
are two unknowns, the amount invested at eight percent (call it E) and the amount invested
at seventeen percent (call it S). We are to solve for E.
.
The problem tells us that the total amount invested is $5000. Ask yourself how this relates
to E and S. The answer is that this $5000 is the sum of E and S. So our first equation is:
.
E + S = 5000
.
The next part of the problem involves the interest. We are told that the total annual interest
made is $490. The interest on E is 8% of E which is the same as 0.08*E. Similarly,
the interest on S, the money invested at 17%, is 17% of S which is the same as 0.17*S.
How does this relate to the total annual interest? The sum of these two amounts of interest
has to add up to be $490. So we can write the equation:
.
0.08*E + 0.17*S = 490
.
There are several ways we can solve these two equations. One of them is substitution,
a method in which we solve one of the equations for one variable in terms of the other
variable. Then we substitute this into the other equation which then only has 1 variable
and can be solved by algebraic means. Let's work this problem out so that you can see
how this method works.
.
Look at the first equation. It says E + S = 5000. Solve this for E by subtracting
S from both sides. The result is E = 5000 - S. We have now solved the first equation
for one variable in terms of another. We could have just as well solved this equation
for S by subtracting E from both sides, but let's go on with what were doing.
.
Now look at the second equation:
.
0.08*E + 0.17*S = 5000
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Since we found out above that E = 5000 - S, let's put 5000 - S into the second equation
in place of E. When we do we get:
.
0.08*(5000 - S) + 0.17*S = 490
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When we multiply out the first term on the left we get:
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400 - 0.08S + 0.17S = 490
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Get rid of the number on the left side by subtracting 400 from both sides of the equation.
When you do that you are left with:
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-0.08S + 0.17S = 90
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Add together the two terms on the left side and you get:
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0.09S = 90
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Finally divide both sides by 0.09 and the result is:
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S = 1000.
.
We now know that $1000 is invested at 17%. And since a total of $5000 was invested,
the remaining money (invested at 8%) is $4,000. That's the answer we were asked to find.
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You may find that the more you talk your way through problems such as these, the easier they
become to understand. Hope this helps you to do just that. You can check the answer
by finding out if 8% of $4000 plus 17% of $1000 adds up to be $490. I think you'll
find that it does.
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