document.write( "Question 73129This question is from textbook
\n" ); document.write( ": Ms. Green invested $1000 at 4% and $6000 at 6%. How much must she invest at 10% to make her total annual income 7.5% of her total investment? \n" ); document.write( "
Algebra.Com's Answer #52391 by bucky(2189)\"\" \"About 
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\n" ); document.write( "Let's work our way through this problem one step at a time:
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\n" ); document.write( "$1000 invested at 4% will return \"1000%2A%28.04%29+=+40\" dollars per year.
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\n" ); document.write( "$6000 invested at 6% will return \"6000%2A%28.06%29+=+360\" dollars per year.
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\n" ); document.write( "Totaled together Ms Green already gets \"360+%2B+40\" = $400 dollars per year on two investments.
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\n" ); document.write( "So far, so good.
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\n" ); document.write( "Now she is going to invest an unknown sum of money (call it S) at 10% so her return on
\n" ); document.write( "this money is going to be \"S%2A%28.10%29\" or in more standard form the number comes before the
\n" ); document.write( "letter. So her return is going to be \"%280.10%29%2AS\"
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\n" ); document.write( "Let's write the total of all the interest she will be getting as:
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\n" ); document.write( "\"400+%2B+%280.10%29%2AS\".
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\n" ); document.write( "What is the total amount she will have invested? We already know about her two investments
\n" ); document.write( "of $1000 and $6000. To that she will add the amount S. So her total investment will be:
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\n" ); document.write( "\"1000%2B6000%2BS\" which reduces to \"S+%2B+7000\"
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\n" ); document.write( "She wants to make 7.5% or 0.075 on this entire investment. So we can write her desired return
\n" ); document.write( "as:
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\n" ); document.write( "\"%280.075%29%2A%28S%2B7000%29\"
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\n" ); document.write( "And we can set that equal to the return she will be getting from her individual investments to
\n" ); document.write( "get:
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\n" ); document.write( "\"%280.075%29%2A%28S%2B7000%29+=+400+%2B+%280.10%29%2AS\"
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\n" ); document.write( "We can solve this equation to find S using normal algebraic operations.
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\n" ); document.write( "First do the distributed multiplication on the left side:
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\n" ); document.write( "\"%280.075%29%2AS+%2B+%280.075%29%2A7000+=+400+%2B+%280.10%29%2AS\"
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\n" ); document.write( "Which further reduces to:
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\n" ); document.write( "\"%280.075%29%2AS+%2B+525+=+400+%2B+%280.10%29%2AS\"
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\n" ); document.write( "Next, to eliminate the 525 on the left side, subtract 525 from both sides to get:
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\n" ); document.write( "\"%280.075%29%2AS+=+-125+%2B+%280.10%29%2AS\"
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\n" ); document.write( "Then to eliminate the S term on the right side, subtract (0.10)*S from both sides. This
\n" ); document.write( "results in:
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\n" ); document.write( "\"%28-0.025%29%2AS+=+-125\"
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\n" ); document.write( "Finally, divide both sides by (-0.025) to solve for S. When you do you finally reach the answer:
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\n" ); document.write( "\"S+=+%28-125%29%2F%28-0.025%29+=+5000\"
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\n" ); document.write( "So Ms Green needs to invest $5000 at 10% to end up with a return rate of 7.5% on the total
\n" ); document.write( "amount she has invested.
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\n" ); document.write( "Hope this helps you to do two things. First to analyze the problem so you can determine
\n" ); document.write( "what to do. And second, to do the mathematical work to find the answer.
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