# 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?

Mar 18, 2018

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: $5 a - 2 w = 74$

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

$a + w - \textcolor{red}{w} = 30 - \textcolor{red}{w}$

$a + 0 = 30 - w$

$a = 30 - w$

Step 2) Substitute $\left(30 - w\right)$ for $a$ in the second equation and solve for $w$:

$5 a - 2 w = 74$ becomes:

$5 \left(30 - w\right) - 2 w = 74$

$\left(5 \times 30\right) - \left(5 \times w\right) - 2 w = 74$

$150 - 5 w - 2 w = 74$

$150 + \left(- 5 - 2\right) w = 74$

$150 - 7 w = 74$

$150 - \textcolor{red}{150} - 7 w = 74 - \textcolor{red}{150}$

$0 - 7 w = - 76$

$- 7 w = - 76$

$\frac{- 7 w}{\textcolor{red}{- 7}} = - \frac{76}{\textcolor{red}{- 7}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 7}}} w}{\cancel{\textcolor{red}{- 7}}} = \frac{76}{\textcolor{red}{7}}$

$w = 10 \frac{6}{7}$

Because you cannot get a question part wrong $\left(\frac{6}{7}\right)$ and part right $\left(\frac{1}{7}\right)$ there is some incorrect or some missing information in this problem,.