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?

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Answer 1 · 2018-03-18T13:27:24

See a solution process below:

First, let's call:

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

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

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

$a + 0 = 30 - w$ $a + 0 = 30 - w$

$a = 30 - w$ $a = 30 - w$

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

$5 a - 2 w = 74$ $5a - 2w = 74$ becomes:

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

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

$150 - 5 w - 2 w = 74$ $150 - 5w - 2w = 74$

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

$150 - 7 w = 74$ $150 - 7w = 74$

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

$0 - 7 w = - 76$ $0 - 7w = -76$

$- 7 w = - 76$ $-7w = -76$

$\frac{- 7 w}{- 7} = - \frac{76}{- 7}$ $(-7w)/color(red)(-7) = -76/color(red)(-7)$

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

$w = 10 6/7$

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,.