Question

A test has 20 questions worth 100 points. The test consists of yes/no questions worth 3 points each and multiple choice questions worth 11 points each. How many yes/no questions are on the test?

Answer 1

Hint: Now we can assume x to be the number of yes/no questions and y to be the number of multiple choice questions. As the total number of questions are 20 we get $x + y = 20$ and as the total worth of questions are 100 we get $3x + 11y = 100$ and solving these equations we get the value of x which is the required number of yes or no questions.

Step by step solution :
We are given that the test contains two types of questions , yes/no questions and multiple choice questions.
Let the number of yes/no questions be x
And let the number of multiple choice questions be y
As we are given that the total number of questions are 20
We get
$ \Rightarrow x + y = 20$ ………….(1)
We are given that the total points of the test is 100
And each yes or no questions is worth 3 points
And each multiple choice question is worth 11 points
Hence we get
$ \Rightarrow 3x + 11y = 100$…………(2)
From (1) we get
$ \Rightarrow x = 20 - y$………(3)
Lets substitute this in (2)
$
   \Rightarrow 3\left( {20 - y} \right) + 11y = 100 \\
   \Rightarrow 60 - 3y + 11y = 100 \\
   \Rightarrow 8y = 100 - 60 = 40 \\
   \Rightarrow y = \dfrac{{40}}{8} = 5 \\
 $
Using this in (3) we get
$ \Rightarrow x = 20 - 5 = 15$

Therefore the number of yes/no questions is 15.

Note :
The linear equations can also be solved using elimination method
At first let's multiply (1) by 3
$ \Rightarrow 3x + 3y = 60$…….(3)
That is let's subtract the equation (3) from (2)
$
  3x + 11y = 100 \\
  \underline { - 3x - 3y = - 60} \\
  0 + 8y = 40 \\
 $
From this we get
$
   \Rightarrow 8y = 40 \\
   \Rightarrow y = \dfrac{{40}}{8} = 5 \\
 $
Substituting this in any one of the equations we get
$
   \Rightarrow x + 5 = 20 \\
   \Rightarrow x = 20 - 5 \\
   \Rightarrow x = 15 \\
 $