document.write( "Question 132062: Jane invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. She received yearly interest of $130. Randy also invested in the same scheme, but he interchanged the amounts invested, and received $4 more as interest. How much amount did each of them invest at different rates?
\n" ); document.write( "Please help me solve this problem. \n" ); document.write( "

Algebra.Com's Answer #96435 by josmiceli(19441) $\"\"$ $\"About$

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Jane invested
\n" ); document.write( "$ $\"a\"$ at 12%
\n" ); document.write( "$ $\"b\"$ at 10%
\n" ); document.write( "-------------
\n" ); document.write( "Randy invested
\n" ); document.write( "$ $\"b\"$ at 12%
\n" ); document.write( "$ $\"a\"$ at 10%
\n" ); document.write( "-------------
\n" ); document.write( "For Jane:
\n" ); document.write( "(1) $\".12a+%2B+.1b+=+130\"$
\n" ); document.write( "For Randy:
\n" ); document.write( "(2) $\".12b+%2B+.1a+=+134\"$
\n" ); document.write( "-------------
\n" ); document.write( "Rewrite (2) as:
\n" ); document.write( " $\".12b+%2B+.1a+=+130+%2B+4\"$
\n" ); document.write( "(3) $\".12b+%2B+.1a+-+4+=+130\"$
\n" ); document.write( "Set the left side of (3) equal to the left
\n" ); document.write( "side of (1)
\n" ); document.write( " $\".12b+%2B+.1a+-+4+=+.12a+%2B+.1b\"$
\n" ); document.write( " $\".02b+-+.02a+=+4\"$
\n" ); document.write( "divide both sides by $\".02\"$
\n" ); document.write( " $\"b+-+a+=+200\"$
\n" ); document.write( " $\"b+=+200+%2B+a\"$
\n" ); document.write( "Substitute this in (1)
\n" ); document.write( " $\".12a+%2B+.1%28200+%2B+a%29+=+130\"$
\n" ); document.write( " $\".12a+%2B+20+%2B+.1a+=+130\"$
\n" ); document.write( " $\".22a+=+110\"$
\n" ); document.write( " $\"a+=+500\"$
\n" ); document.write( " $\"b+=+200+%2B+a\"$
\n" ); document.write( " $\"b+=+700\"$
\n" ); document.write( "Jane invested
\n" ); document.write( "$ $\"500\"$ at 12%
\n" ); document.write( "$ $\"700\"$ at 10%
\n" ); document.write( "-------------
\n" ); document.write( "Randy invested
\n" ); document.write( "$ $\"700\"$ at 12%
\n" ); document.write( "$ $\"500\"$ at 10%
\n" ); document.write( "check answers:
\n" ); document.write( "(1) $\".12a+%2B+.1b+=+130\"$
\n" ); document.write( " $\".12%2A500+%2B+.1%2A700+=+130\"$
\n" ); document.write( " $\"60+%2B+70+=+130\"$
\n" ); document.write( " $\"130+=+130\"$
\n" ); document.write( "-------------
\n" ); document.write( "(2) $\".12b+%2B+.1a+=+134\"$
\n" ); document.write( " $\".12%2A700+%2B+.1%2A500+=+134\"$
\n" ); document.write( " $\"84+%2B+50+=+134\"$
\n" ); document.write( " $\"134+=+134\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );