word problem help please?

Question

question: jordan answered all of the questions on a 20-question test. A score on the test is computed by adding 5 points for every correct answer and subtracting 1 point for every wrong answer. If Jordan's score was 82, how many questions did he answer correctly??

please help..so lost.
show procedure pleaseeeeee.
thank you =]

Answer 1

let no of correct ans be x
no of wrong ans be y
let us make 2 linear equations.
5 marks for every correct ans.
so,5x
1 mark for every wrong ans,so,1y= y
total score = 82
so we have,
5x - y = 82 -----> (1)
since total no of questions = 20,
it contains both correct and wrong answers.
so, we have,
x + y = 20 ------->(2)

add (1) and (2)
we have,
5x - y = 82
x + y = 20
(y gets cancelled)
6x = 102
implies, x = 17

since x + y = 20,
17 + y = 20
implies, y = 20 - 17 = 3
so, y = 3.

we have, x = 17, y = 3
so
no.of correct ans = 17 and no. of wrong ans= 3.

Answer 2

Let c denote a correct answer, then (20 - c) represents the number of wrong answers, because all the questions were answered.

5c - (20 - c) = 82
5c - 20 + c = 82
6c = 82 + 20 = 102
c = 102/6 = 17 correct answers.

Ck (17)5 - 3 = 85 - 3 = 82.

Answer 3

Well, let's see...let x=the number of correct answers, so (20-x)= the number of wrong answers, right? So his total score=82=5x-1(20-x), right? So 82=5x-20+x, right? So 82=6x-20, right? So 82+20=6x, right? That means x=102/6, right? So x=34/2, so x=17 correct answers, and 3 wrong answers, right? Let's try it: 17 times 5 equals 85 minus 3 times 1 equals 82!!!. It works!!!
P.S. You don't need a two variable analysis to solve this problem. Don't be fooled by anyone who says you do, such as the ones below.

Answer 4

If he answered 17 questions correctly out of 20 that would give him 85 points, and that would mean that he answered 3 questions incorrectly, so you would subtract 3 points from 85 and leave you with 82 points. Hope this helps.

Answer 5

x + y = 20 (x=correct answers, y=wrong answers)
5x - y = 82 (5 points for every right answer, minus 1 for every wrong, gave him 82 points)

Solve the system.. [elimination]
Add the second equation to the first, which will cancel out the y's. So,
6x = 102
x = 17

He answered 17 questions correctly.

Hope that helped! I did my best explaining! =]

Answer 6

c= # correct
w= # wrong

c + w = 20

c*5 + w *(-1)= 82

Two equations in two variables.

Add the first to the second:

6*c = 102
c= 17 So, w=3

Test it:

17*5 - 3 = 85 -3 = 82

Done!

Answer 7

Set up a system of equations:

x represents correct answers and y represents wrong answers

x+y=20
5x-y=82

Solve by elimination:

you cancel out y already so add the equations:
6x=102
x=17

plug 17 into one of the above equations for x and you get 3 for y.

so he answered 17 questions right and 3 questions wrong

Answer 8

he answers 17 questions right, so if he got 17 questions right, 17x5=85, then he got 3 questions wrong 85-3=82,

he answered all of the questions
he got an 82%
he got 17 questions right
he got 3 answers wrong
you got this question answered
you got this question answered right

Answer 9

ok.. you need a few equations

so you know there are 20 questions, and he either got right answers or wrong answers, lets say he got x number of right answeres and y number of wrong answers

so we know the total number of questions is 20, we also knwo the total number of right answers and teh total number of wrong answers must add to 20
so...
x+y=20
ok, now you know that he got 5 pts for every right answer, and took 1 pt away for every wrong answer, so we could say
5x-1y = 82

now we have 2 equations and 2 unknowns

x+y=20
5x-y=82
solve by elimination, so add both equations together
6x+0y=102
6x=102
x=17

and we know that x+y=20
so
17+y=20
y=3

so he got 17 right answers and 3 wrong ones

hope this helps,
matttlocke

Answer 10

w= wrong ansers
r=right answers

r+w= 20
5r-w=82

6r= 102
r= 17
w= 3