document.write( "Question 1126126: Mr. and Mrs. Garcia have a total of $100,000 to be invested in stocks, bonds, and a money market account. The stocks have a rate of return of 12%/year, while the bonds and the money market account pay 8%/year and 4%/year, respectively. The Garcias have stipulated that the amount invested in the money market account should be equal to the sum of 20% of the amount invested in stocks and 10% of the amount invested in bonds. How should the Garcias allocate their resources if they require an annual income of $10,000 from their investments? \n" ); document.write( "

Algebra.Com's Answer #742462 by ikleyn(52862) $\"\"$ $\"About$

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document.write( "Let x be the sum invested in the money market.\r\n" );
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document.write( "Then the sum invested in stocks should be 5x, The the sum invested in bonds should be 10x, according to the condition.\r\n" );
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document.write( "The total investments equation is\r\n" );
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document.write( "    x + 5x + 10x = 100000      dollars,\r\n" );
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document.write( "which gives\r\n" );
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document.write( "    16x = 100000,  and hence\r\n" );
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document.write( "    x =  = 6250  dollars.\r\n" );
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document.write( "Thus the investments should be  $6250 in money market;  $6250*5 = $31250 in stocks  and  $6250*10 = $62500  in bonds.\r\n" );
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document.write( "Now, let us check the annual income.  At calculated investments, it should be\r\n" );
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document.write( "    0.04*6250 + 0.08*62500 + 0.12*31250 = 9000 dollars.\r\n" );
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document.write( "It shows that at given conditions the problem HAS NO solution.\r\n" );
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document.write( "Answer.  The problem is over-defined; in other words, it has TOO MANY conditions that do not agree each other.\r\n" );
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document.write( "         Therefore, at given conditions the problem HAS NO solution.\r\n" );
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