document.write( "Question 527491: 3. To stimulate his daughter in the pursuit of problem solving, a math professor offered to pay her $8 for every equation correctly solved and to fine her $5 for every incorrect solution. At the end of the first 26 problems of the problem set, neither owed any money to the other. How many problems did the daughter solve correctly? \n" ); document.write( "

Algebra.Com's Answer #348925 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = number of correct solutions
\n" ); document.write( "Let $\"b\"$ = number of incorrect solutions
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+8a+-+5b+=+0+\"$
\n" ); document.write( "(2) $\"+a+%2B+b+=+26+\"$
\n" ); document.write( "------------
\n" ); document.write( "Multiply both sides of (2) by $\"5\"$
\n" ); document.write( "and add the equations
\n" ); document.write( "(1) $\"+8a+-+5b+=+0+\"$
\n" ); document.write( "(2) $\"+5a+%2B+5b+=+130+\"$
\n" ); document.write( " $\"+13a+=+130+\"$
\n" ); document.write( " $\"+a+=+10+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(2) $\"+a+%2B+b+=+26+\"$
\n" ); document.write( "(2) $\"+10+%2B+b+=+26+\"$
\n" ); document.write( "(2) $\"+b+=+16+\"$
\n" ); document.write( "The daughter solved 10 equations correctly
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+8a+-+5b+=+0+\"$
\n" ); document.write( "(1) $\"+8%2A10+-+5%2A16+=+0+\"$
\n" ); document.write( "(1) $\"+80++-+80+=+0+\"$
\n" ); document.write( " $\"+0+=+0+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );