document.write( "Question 579126: Your science test is worth 100 points and contains 38 questions.There are two-point and five-point questions on the test.How many of each type of question are on the test? \n" ); document.write( "

Algebra.Com's Answer #370870 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = number of 2-point questions
\n" ); document.write( "Let $\"+b+\"$ = number of 5-point questions
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+38+\"$
\n" ); document.write( "(2) $\"+2a+%2B+5b+=+100+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "Multiply both sides of (1) by $\"2\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+2a+%2B+5b+=+100+\"$
\n" ); document.write( "(1) $\"+-2a+-+2b+=+-76+\"$
\n" ); document.write( " $\"+3b+=+24+\"$
\n" ); document.write( " $\"+b+=+8+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+8+=+38+\"$
\n" ); document.write( "(1) $\"+a+=+30+\"$
\n" ); document.write( "There are 30 of the 2-point questions
\n" ); document.write( "There are 8 of the 5-point questions
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+2%2A30+%2B+5%2A8+=+100+\"$
\n" ); document.write( "(2) $\"+60+%2B+40+=+100+\"$
\n" ); document.write( "(2) $\"+100+=+100+\"$
\n" ); document.write( "OK \n" ); document.write( "

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