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?

1 Answer
Mar 18, 2018

Answer:

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,.