document.write( "Question 648173: A student takes a test where 3 points are given for every correct answer and 2 points are deducted for every wrong answer. If the students scores 55 points on a 40 question test, how many questions did she answer correctly? \n" ); document.write( "
Algebra.Com's Answer #406585 by DrBeeee(684)\"\" \"About 
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Let r = number of problems answered correctly
\n" ); document.write( "Let w = number of problems answered incorrectly
\n" ); document.write( "From the problem statements we have
\n" ); document.write( "(1) r + w = 40, that is there were 40 total problem.
\n" ); document.write( "(2) 3*r - 2*w = 55, the grade is +3 for each correct answer and -2 for each incorrect answer. Make sense?
\n" ); document.write( "Solve (1) and (2) simultaneously.
\n" ); document.write( "Let's substitute r from (1) in (2);
\n" ); document.write( "(3) r = 40 - w
\n" ); document.write( "Then (2) becomes
\n" ); document.write( "(4) 3*(40-w) - 2*w = 55 or
\n" ); document.write( "(5) 120 -3*w - 2*w = 55 or
\n" ); document.write( "(6) 5*w = 65 or
\n" ); document.write( "(7) w = 13
\n" ); document.write( "Then from (3)
\n" ); document.write( "(8) r = 27
\n" ); document.write( "Is this correct? Let's see. Use (2),
\n" ); document.write( "Is (3*27 - 2*13 = 55)?
\n" ); document.write( "Is (81 - 26 = 55)?
\n" ); document.write( "Is (55 = 55)? Yes
\n" ); document.write( "Answer: The student missed 13 questions, but answered 27 correctly! \n" ); document.write( "
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