document.write( "Question 177563: Dr. Smith's chemistry midterm has 60 questions. She scores the test as follows: for each correct answer, she gives 2 points; for each incorrect answer, she subtracts 2/3 of a point; for unanswered questions, she neither gives nor subtracts points. If Andrew scored a 68 and did not answer 2 of the questions, how many questions did he answer correctly? \n" ); document.write( "

Algebra.Com's Answer #132573 by Mathtut(3670) $\"\"$ $\"About$

You can put this solution on YOUR website!
let a,b,and c be the number of correct,incorrect,and unanswered questions, respectively
\n" ); document.write( ":
\n" ); document.write( "a+b+c=60.....eq 1
\n" ); document.write( "c=2..........eq 2
\n" ); document.write( "2a-(2/3)b=68.eq 3
\n" ); document.write( ":
\n" ); document.write( "lets plug value of c in eq 2 into eq 1
\n" ); document.write( ":
\n" ); document.write( "a+b+2=60--->a+b=58
\n" ); document.write( ":
\n" ); document.write( "a+b=58........revised eq 1
\n" ); document.write( "2a-(2/3)b=68..eq 3
\n" ); document.write( ":
\n" ); document.write( "multiply revised eq 1 by -2 and add the two equations together so as to eliminate the a terms. We are left with -2b-(2/3)b=-116+68
\n" ); document.write( ":
\n" ); document.write( "(-8/3)b=-48
\n" ); document.write( ":
\n" ); document.write( "-8b=-144
\n" ); document.write( ":
\n" ); document.write( " $\"b=18\"$
\n" ); document.write( ":
\n" ); document.write( " $\"a=58-b=58-18=highlight%2840%29\"$ number of correct answers \n" ); document.write( "

\n" );