document.write( "Question 81743: Bob invested $21,000, part at 20% and part at 17%. If the total interest at the end of the year is $3,780, how much did he invest at 20%? \n" ); document.write( "
Algebra.Com's Answer #58565 by bucky(2189)\"\" \"About 
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Let T represent the amount of money invested at 20%.
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\n" ); document.write( "Let S represent the amount of money invested at 17%
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\n" ); document.write( "From the problem, we can tell that T + S must equal the total investment of $21,000.
\n" ); document.write( "In equation form we can write this as:
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\n" ); document.write( "T + S = 21000
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\n" ); document.write( "This is one equation we can use.
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\n" ); document.write( "Next we know that the amount of interest on T is 20% of T or 0.2*T. We also know that the
\n" ); document.write( "amount of interest on S is 17% of S or 0.17*S. If we add these two amounts of interest
\n" ); document.write( "we get the total interest of $3780. In equation form this is:
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\n" ); document.write( "0.2*T + 0.17*S = 3780
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\n" ); document.write( "This is the second equation we can use.
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\n" ); document.write( "The problem asks us to solve for T, the amount of money invested at 20%. Suppose we return
\n" ); document.write( "to the first equation and solve it for S in terms of T.
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\n" ); document.write( "The first equation is T + S = 21000. Let's subtract T from both sides of the equation and
\n" ); document.write( "when we do, we get that S = 21000 - T.
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\n" ); document.write( "Next return to the second equation and for S in that equation let's substitute its equivalent,
\n" ); document.write( "21000 - T.
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\n" ); document.write( "With that substitution, the second equation becomes:
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\n" ); document.write( "0.2*T + 0.17*(21000 - T) = 3780
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\n" ); document.write( "Do the distributed multiplication on the left side by multiplying 0.17 times each of
\n" ); document.write( "the terms in the parentheses. When you do that you get:
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\n" ); document.write( "0.2*T + 3570 - 0.17T = 3780
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\n" ); document.write( "If you combine the two terms that contain T by subtracting 0.17 from 0.2 the equation
\n" ); document.write( "becomes:
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\n" ); document.write( "0.03*T + 3570 = 3780
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\n" ); document.write( "Next, get rid of the 3570 on the left side by subtracting 3570 from both sides. After this
\n" ); document.write( "subtraction, the resulting equation is:
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\n" ); document.write( "0.03*T = 210
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\n" ); document.write( "Solve for T by dividing both sides of this equation by 0.03. When you do that, the equation
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\n" ); document.write( "T = 210/0.03 = 7000
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\n" ); document.write( "So the answer is that $7,000 is invested at 20% and therefore the remaining $14,000 is
\n" ); document.write( "invested at 17%.
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\n" ); document.write( "We can quickly check this. If $7,000 is invested at 20% then this produces $1400 of
\n" ); document.write( "interest (0.2*7000). Then if $14,000 is invested at 17%, this produces $2380 of interest (0.17*14000).
\n" ); document.write( "The total interest is then $1400 + $2380 = $3780 and this is the amount that the problem
\n" ); document.write( "said it should be. Therefore, our solution is good. The money invested at 20% is $7,000.
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\n" ); document.write( "Hope this helps you to understand the problem. \n" ); document.write( "
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