right answer 3 points. wrong answer -5 points. answered 25 quiz questions. got 27 points.how many more correct answers than incorrect answers did Randi have

Question

im not understanding how to solve this problem and where to start

 

Answer 1

Let n be either the number of right or wrong answers. You'll see it works either way.

With 25 TOTAL answers the OTHER possibility must be '25 minus n'.

 

Using n for right(+3) answers

 

3n + (-5(25 - n)) = 27

3n + (-125 + 5n) = 27 [Careful: -5 times -n equals 5n]

3n + 5n - 125 =27

8n - 125 = 27 [Adding 125 to both sides]

8n = 152 [Dividing each by 8]

n = 19 Correct answers.

 

Using n for wrong(-5) answers (same process)

3(25 - n) + -5n = 27

75 - 3n -5n = 27

75 - 8n = 27

8n -75 = -27

8n = 48

n = 6 Incorrect answers.

 

19 plus 6 is 25 total question.

 

The difference being 13 more correct.

Answer 2

We need to figure out how many correct and incorrect answers Randi got.  Then we compare them by subtracting.

 

 

Let x = number of correct answers

Let y = number of incorrect answers

 

 

Set up equations using the information given.  Note that -5 indicates that he loses 5 points.

 

3x - 5y = 27                  eq1

x + y = 25                     eq2

 

 

We have a system of equations with two equations with two unlike variables.

 

Multiply eq2 by 3.  Keep eq1 as it is.

 

3x - 5y = 27           eq1

3x + 3y = 75           eq2

 

 

Subtract eq2 from eq1 to eliminate the x terms.

 

-8y = -48

 

y = 6

 

 

If he got 6 questions incorrect, then he got 19 questions correct.  Now we subtract.

 

19 - 6 = 13

 

 

Randi had 13 more correct answers than wrong answers.

Answer 3

let there are x correct answers and then incorrect answers will be (25-x)

 

total points scored will be given by equation:

 

(3*x) -[5*(25-x) = 27

3x - (125 - 5x) = 27

 3x - 125 + 5x = 27

         8x = 27 +125 

         8x = 152

         x  =  152/8 = 19

 

correct answers : x= 19

incorrect answers : 25 - x = 25-19 = 6

 no. of correct answers more than incorrect answers = 19 -6 = 13