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tom took a 30 question test. he got 5 pts for correct answers and lost 1 pt. for incorrect ones. He scored 120 points. how many correct ones did he get?

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Joyce, hello.  This is a word problem that represents a two by two system of linear equations.  First let x be the number of questions answered correctly and let y be the number of questions answered incorrectly.  Then translate the information into two equations both involving x and y.  Since there are a total of 30 questions we get x+y=30.  The second equation pertains to the point values.  Since he score a total of 120 points we get 5x-1y=120.  We can solve this system algebraically by substitution or by elimination.  Here, the elimination method is easier.  Simply add the two equations together vertically.  We get 6x=150.  The y's cancel out.  Solving 6x=150 for x, we get that x=25.  Since x represents the number answered correctly, we are done.  The answer is 25 questions.