document.write( "Question 802468: a professor has two types of problems to use in putting together a test: multiple choice questions worth 1 point each and short answer questions worth 8 points each. If the professor wants to create a 130 point test using a total of 74 questions, then how many question of each type should she use? \n" ); document.write( "

Algebra.Com's Answer #483890 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+a+\"$ = number of $\"+1+\"$ point questions
\n" ); document.write( "Let $\"+b+\"$ = number of $\"+8+\"$ point questions
\n" ); document.write( "-----------
\n" ); document.write( "(1) $\"+a+%2B+b+=+74+\"$
\n" ); document.write( "(2) $\"+1%2Aa+%2B+8%2Ab+=+130+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"+a+%2B+8b+=+130+\"$
\n" ); document.write( "(1) $\"+-a+-+b+=+-74+\"$
\n" ); document.write( " $\"+7b+=+56+\"$
\n" ); document.write( " $\"+b+=+8+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+8+=+74+\"$
\n" ); document.write( "(1) $\"+a+=+66+\"$
\n" ); document.write( "66= number of $\"+1+\"$ point questions
\n" ); document.write( "8 = number of $\"+8+\"$ point questions
\n" ); document.write( "---------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+66+%2B+8%2A8+=+130+\"$
\n" ); document.write( "(2) $\"+66+%2B+64+=+130+\"$
\n" ); document.write( "(2) $\"+130+=+130+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "
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