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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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2 Answers

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.
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?
Solution:
Let x be the number of correct responses and y be the number of incorrect responses
x+y=30 ----------------- eq.1
Since he is given 5 points for each correct answer and he loss 1 point for each incorrect response then 
5x-y=120--------- eq 2
Adding both equations 6x=150, and x= 150/6=25,
Substituting value for x in equation 1 then 25+y=30 and then y =5.
Tom got 25 correct responses.
 
THIS PROBLEM COULD BE SOLVE USING A RATIO TABLE
 
NUMBER CORRECT AND POINTS (A)            NUMBER INCORRECT AND POINTS (B)                 POINTS (A-B)
30 --- (30X5) =150                                    0------- 0x1                                                       150
29      (29 X 5)=145                                  1--------1X1  =1                                                  144
28      (28 X5) =140                                  2-------- 2 X1=2                                                  138
27      (27x5) = 135                                  3----------3x1=3                                                  132
26      (26 x5) = 130                                 4--------- 4x1 =4                                                  126
25      (25x5)=125                                    5----------5x1=5                                                  120
 
Based on the table he scored 120 points which is the result of having 25 correct responses corect.