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Your teacher is giving you a test worth 100 points containing 40 questions. There are two point and four point questions on the test. How many of each type of question are on the test?
\n" ); document.write( "Let the number of 2-point questions be T
\n" ); document.write( "and let the number of 4-point questions be F
\n" ); document.write( "Total number of questions = 40
\n" ); document.write( "Therefore T + F = 40 ----(1)
\n" ); document.write( "Total number of points = 100
\n" ); document.write( "That means total points out of 2-point questions
\n" ); document.write( "together with the total points out of 4-point questions is 100
\n" ); document.write( "That 2T + 4F = 100 ----(2)
\n" ); document.write( "[one 2-point question = 2-points
\n" ); document.write( "and therefore T, 2-point questios = 2XT = 2T points
\n" ); document.write( "one 4-point question = 4-points
\n" ); document.write( "and therefore F, 4-point questios = 4XF = 4F points]
\n" ); document.write( "(1) implies T = (40-F) ----(*)
\n" ); document.write( "Putting (*) in (2)
\n" ); document.write( "2T+4F = 100
\n" ); document.write( "2(40-F)+4F = 100
\n" ); document.write( "80-2F+4F = 100
\n" ); document.write( "(-2F+4F)= 100-80 (grouping like terms,changing sign while changing side)
\n" ); document.write( "2F = 20
\n" ); document.write( "F = 20/2 = 10
\n" ); document.write( "Therefore the number of 4-point questions = 10
\n" ); document.write( "Putting F= 10 in (*),
\n" ); document.write( "T = 40-F = 40-10 = 30
\n" ); document.write( "Therefore the number of 2-point questions =30
\n" ); document.write( "Verification:30 questions each of 2-points give 30X2 = 60
\n" ); document.write( "10 questions each of 4-points give 10X4 = 40
\n" ); document.write( "These points add up to 100.
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