document.write( "Question 115895: Ms. Mills invested her $20,000 bonus in two accounts. She took a 4% loss on one investment and made a 12% profit on another investment, but ended up breaking even. How much was invested in each account? \n" ); document.write( "

Algebra.Com's Answer #84350 by Fombitz(32388) $\"\"$ $\"About$

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Let's call the amount at 4%, F, and at 12%, T.
\n" ); document.write( "Here's what you know.
\n" ); document.write( "1. $\"F%2BT=20000\"$ Total is $20,000.
\n" ); document.write( "Gain is positive interest, loss is negative interest.
\n" ); document.write( "2. $\"-0.04F%2B0.12T=0\"$ Interest from both broke even (totaled zero).
\n" ); document.write( "Let solve equation 2 for F in terms of T.
\n" ); document.write( "2. $\"-0.04F%2B0.12T=0\"$
\n" ); document.write( " $\"-0.04F=-0.12T\"$
\n" ); document.write( " $\"F=0.12T%2F0.04\"$
\n" ); document.write( " $\"F=3T\"$
\n" ); document.write( "Now substitute that value in equation 1 and solve for T.
\n" ); document.write( "1. $\"F%2BT=20000\"$
\n" ); document.write( " $\"3T%2BT=20000\"$
\n" ); document.write( " $\"4T=20000\"$
\n" ); document.write( " $\"T=5000\"$
\n" ); document.write( "and
\n" ); document.write( " $\"F=3T\"$
\n" ); document.write( " $\"F=3%285000%29\"$
\n" ); document.write( " $\"F=15000\"$
\n" ); document.write( "Check the answers
\n" ); document.write( "1. Total is $20,000
\n" ); document.write( "2. Loss at 4% = (0.04)(15,000) = -6,000
\n" ); document.write( "Gain at 12% = (0.12)(5,000) = 6,000
\n" ); document.write( "Sum is zero.
\n" ); document.write( "Good answers.
\n" ); document.write( "$5,000 at 4% and $15,000 at 12%. \n" ); document.write( "

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