Question 70101: Please solve the following word problem:
Bob invested $20,000, part at 14% and part at 13%. If the total interest at the end of the year is $2,720, how much did he invest at 14%?
Found 3 solutions by stanbon, ptaylor, bucky:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Bob invested $20,000, part at 14% and part at 13%. If the total interest at the end of the year is $2,720, how much did he invest at 14%?
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Let amt. invested at 14% be "x"; interest on this is 0.14x
Amt. invested at 13% is "20,000-x"; interest on this is 0.13(20000-x)
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EQUATION:
interest + interest = 2720 dollars
0.14x + 0.13(20000-x)=2720
14x 13(20000-x) = 272000
14x+260000-13x = 272000
x=12000 dollars (this is the amt. invested at 14%)
Cheers,
Stan H.
Answer by ptaylor(2198)  (Show Source):
You can put this solution on YOUR website! Let x= amount at 14%
Then 20000-x=amount at 13%
I=PRT where T=1 So our equation to solve:
0.14x+0.13(20000-x)=2720 get rid of parens
0.14x+2600-0.13x=2720 subtract 2600 from both sides
0.01x=2720-2600
0.01x=120 divide both sides by 0.01
x=$12000 --------------------------------amount invested at 14%
20000-x=20000-12000=$8000----amount invested at 13%
Ck
12000(.14)+8000(.13)=2720
1680+1040=2720
2720=2720
Hope this helps----ptaylor
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Bob invested $20,000, part at 14% and part at 13%. If the total interest at the end of
the year is $2,720, how much did he invest at 14%?
It takes two equations to solve this equation. But before beginning, let's define F as the
amount of money invested at 14% and T as the amount invested at 13%.
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Since the total amount of money invested is $20,000 we can add F and T and set that sum
equal to the $20,000. In equation form this first one of two our equations becomes:
.
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The problem tells you the interest Bob makes on the amount F is 14% of F. You can write
this as:
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Interest on F = 0.14*F
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Similarly the interest Bob makes on the amount T is 13% of T. You can write this as:
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Interest on T = 0.13*T.
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These two amounts of interest have to add up to be the total annual interest of $2,720
In equation form this becomes:
.
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This is the second of the equations that you can use to solve this problem.
There are several ways that you could solve this system of two equations. Let's use the
substitution method. Return to the first equation and see that it can be solved for F
by subtracting T from both sides. If you do that subtraction you get:
.
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Now substitute that value for F into your second equation to get:
.
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Multiplying out the first term on the left side results in:
.
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Add the two terms containing T. That sum is -0.01T and it replaces the two terms,
resulting in the equation:
.
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Now subtract 2800 from both sides to eliminate the 2800 on the left side. When you subtract
it from the right side (2720 - 2800) the result is -80. Therefore, the equation is reduced to:
.
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Multiply both sides by -1 to eliminate the negative signs and get:
.
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Finally divide both sides by 0.01 (or you can multiply both sides by 100 also) and the
equation becomes:
.
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Since you now know that T = $8,000 and the total amount invested is $20,000 you also know
that the amount invested at 14% (F) has to be $12,000. So the answer you were looking for
is $12,000.
Let's check it:
Do F and T add up to be $20,000?
.
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That works. Then does 14% of F and 13% of T add up to be $2720?
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0.14*(12000) + 0.13(8000) = 2720}}}
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Do the multiplications on the left side:
.
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The left side does add up to equal the right side, so this works also. The problem is
correct and you know that the answer of $12,000 is correct for the amount invested
at 14%.
.
Hope that this helps you understand the problem a little better, and aids you in figuring
out when you are given two different limits on the problem (in this case the limits of
the total amount of interest and the total amount invested) that you are likely going to
need to solve two equations to get the answer.
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