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