document.write( "Question 825987: We invested $10,000 in 2 bank accounts. One account earns 14% per year the other earns 8% per year. How much did we invest into each account if after the first year, the combined interest from the 2 accounts is $1238? \n" ); document.write( "
Algebra.Com's Answer #497825 by math-vortex(648) $\"\"$ $\"About$
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "We invested $10,000 in 2 bank accounts. One account earns 14% per year the other earns 8% \r\n" );
document.write( "per year. How much did we invest into each account if after the first year, the combined \r\n" );
document.write( "interest from the 2 accounts is $1238?\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "Define Variables:\r\n" );
document.write( "Let x be the amount you originally invested in the first account.\r\n" );
document.write( "Let y be the amount you originally invested in the second account.\r\n" );
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document.write( "Write Expressions and Equations:\r\n" );
document.write( "Since you invested a total of $10,00 in two accounts. An equation that represents this is\r\n" );
document.write( "x + y = 10000\r\n" );
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document.write( "One account (say the first one) earns 14% per year. Recall that the decimal form of 14% is\r\n" );
document.write( "0.14. An expression for the amount of interest you earn after the first year in this account is\r\n" );
document.write( "0.14x.\r\n" );
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document.write( "The other account earns 8% per year. The decimal representation of 8% is 0.08. The amount \r\n" );
document.write( "of interest you earn after one year in this account is 0.08y.\r\n" );
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document.write( "The combine interest from both account after one year is $1238. An equation representing\r\n" );
document.write( "the total interest earned is\r\n" );
document.write( "0.14x + 0.08y = 1238\r\n" );
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document.write( "Now we have a system of two equations with two variables. We can solve for x and y. Rewrite\r\n" );
document.write( "the first equation in \"y=\" form.\r\n" );
document.write( "x + y = 10000\r\n" );
document.write( "y = 10000 - x\r\n" );
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document.write( "Substitute 10000-x for y in the second equation.\r\n" );
document.write( "0.14x + 0.08y = 1238\r\n" );
document.write( "0.14x + 0.08(10000 - x) = 1238\r\n" );
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document.write( "Solve this equation for x. Use the Distributive Property to clear parentheses.\r\n" );
document.write( "0.14x + 800 - 0.08x = 1238\r\n" );
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document.write( "Combine like terms (0.14x-0.08x is 0.06x).\r\n" );
document.write( "0.06x + 800 = 1238\r\n" );
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document.write( "Subtract 800 to both sides to isolate x on the left.\r\n" );
document.write( "0.06x = 1238 - 800\r\n" );
document.write( "0.06x = 438\r\n" );
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document.write( "Divide both sides of the equation by 0.06.\r\n" );
document.write( "x = 438/0.06\r\n" );
document.write( "x = 7300\r\n" );
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document.write( "In the context of this problem, x=7300 means that you invested $7300 in the first account.\r\n" );
document.write( "Since you invested a total of $10000, you invested 10000-7300=$2700 in the second account.\r\n" );
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document.write( "Check your work by verifying that these amounts will yield the correct amount of interest.\r\n" );
document.write( "Substitute 7300 for x and 2700 for y in the interest equation.\r\n" );
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document.write( "0.14x + 0.08y = 1238\r\n" );
document.write( "0.14(7300) + 0.08(2700) = 1238\r\n" );
document.write( "1022 + 216 = 1238\r\n" );
document.write( "1238 = 1238 \r\n" );
document.write( "Check!\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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