document.write( "Question 198412: Donna invested her 33000 bonus, and received a total of 970 in interest after one year. If part of the money returned 4% and the remainding 2.25%. then how much did she invest at each rate? \n" ); document.write( "

Algebra.Com's Answer #148937 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = amount invested @ 4%
\n" ); document.write( "Let $\"b\"$ = amount invested @ 2.25%
\n" ); document.write( " $\".04a+%2B+.0225b+=+970\"$
\n" ); document.write( "Multiply both sides by $\"10000\"$
\n" ); document.write( "(1) $\"400a+%2B+225b+=+9700000\"$
\n" ); document.write( " $\"a+%2B+b+=+33000\"$
\n" ); document.write( "Multiply both sides by $\"225\"$
\n" ); document.write( "(2) $\"225a+%2B+225b+=+7425000\"$
\n" ); document.write( "Subtract (2) from (1)
\n" ); document.write( "(1) $\"400a+%2B+225b+=+9700000\"$
\n" ); document.write( "(2) $\"-225a+-+225b+=+-7425000\"$
\n" ); document.write( " $\"175a+=+2275000\"$
\n" ); document.write( " $\"a+=+13000\"$
\n" ); document.write( "And, since
\n" ); document.write( " $\"a+%2B+b+=+33000\"$
\n" ); document.write( " $\"13000+%2B+b+=+33000\"$
\n" ); document.write( " $\"b+=+20000\"$
\n" ); document.write( "She invested $13,000 @ 4% and $20,000 @ 2.25%
\n" ); document.write( "check:
\n" ); document.write( " $\".04a+%2B+.0225b+=+970\"$
\n" ); document.write( " $\".04%2A13000+%2B+.0225%2A20000+=+970\"$
\n" ); document.write( " $\"520+%2B+450+=+970\"$
\n" ); document.write( " $\"970+=+970\"$
\n" ); document.write( "OK \n" ); document.write( "

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