Question

Afla took part in a quiz which he had to answer 30 questions. 5 marks were awarded for each correct answer and 2 marks were deducted for each wrong answer. Afla scored a total of 74 marks for the quiz. How many answeres did he mess up?

Answer 1

See a solution process below:

Explanation:

First, let's call:

• The number of correct answers: `a`
• The number of wrong answers: `w`

Next, from the information in the problem we can write two equations:

• Equation 1: `a + w = 30`

• Equation 2: `5a - 2w = 74`

Step 1) Solve the first equation for `a`:

`a + w - color(red)(w) = 30 - color(red)(w)`

`a + 0 = 30 - w`

`a = 30 - w`

Step 2) Substitute `(30 - w)` for `a` in the second equation and solve for `w`:

`5a - 2w = 74` becomes:

`5(30 - w) - 2w = 74`

`(5 xx 30) - (5 xx w) - 2w = 74`

`150 - 5w - 2w = 74`

`150 + (-5 - 2)w = 74`

`150 - 7w = 74`

`150 - color(red)(150) - 7w = 74 - color(red)(150)`

`0 - 7w = -76`

`-7w = -76`

`(-7w)/color(red)(-7) = -76/color(red)(-7)`

`(color(red)(cancel(color(black)(-7)))w)/cancel(color(red)(-7)) = 76/color(red)(7)`

`w = 10 6/7`

Because you cannot get a question part wrong `(6/7)` and part right `(1/7)` there is some incorrect or some missing information in this problem,.