document.write( "Question 476566: Next week your math teacher is giving a chapter test worth 100 points. The test will consist of 35 problems. Some problems are worth 2 points and some problems are worth 4 points. How many problems of each value are on the test?) \n" ); document.write( "
Algebra.Com's Answer #326770 by Theo(13342)\"\" \"About 
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let x = number of questions that are 2 points each.
\n" ); document.write( "let y = number of questions that are 3 points each.
\n" ); document.write( "since the total number of questions is 35, then your first equation is:
\n" ); document.write( "x + y = 35
\n" ); document.write( "since each x gets you 2 points and each y gets you 3 points, then your ssecond equation is:
\n" ); document.write( "2x + 3y = 100
\n" ); document.write( "solve these 2 equations simultaneously for your answer.
\n" ); document.write( "use second equation to solve for y in terms of x.
\n" ); document.write( "you get y = 35 - x
\n" ); document.write( "substitute for y in the first equation to get:
\n" ); document.write( "2x + 3(35-x) = 100 which becomes:
\n" ); document.write( "2x + 105 - 3x = 100 which becomes:
\n" ); document.write( "-x + 105 = 100
\n" ); document.write( "add x to both sides of this equation and subtract 100 from both sides of this equation to get:
\n" ); document.write( "x = 5
\n" ); document.write( "since x + y = 35, this means that y = 30
\n" ); document.write( "you have 5 questions that are 2 points each and 30 questions that are 3 points each for a total of 5 + 30 = 35 questions with a total of 10 + 90 = 100 points.\r
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