Question

An instructor scored a student’s test of $50$ questions by subtracting $2$ times the number of incorrect answers from the number of correct answers. If the score is $26$, find the number of right answers.

Answer 1

Hint: In this question, assume two variables for correct and incorrect answers. On the given information make two equations in the form of $p$ and $q$, and then by solving these two equations get the values of variables and get the number.

Complete step-by-step solution:
A word problem is a practice of mathematics in which the significant information on the problem is presented in an ordinary manner rather than in mathematical expression.
The liable way to solve the word problem is to represent unknown numbers as variables, convert the rest of the word problem into a mathematical expression and then finally solve the problem.
Let $p$ be the number of correct answers and let $q$ be the number of incorrect answers. The total number of questions is the sum of correct and incorrect answers.
The total number of questions are the sum of correct and incorrect answers and it can be written as,
$p + q = 50......\left( 1 \right)$
Student’s test scored by an instructor is the difference of $p$ from two times of $q$ that is written as,
$p - 2q = 26......\left( 2 \right)$
Now we add the equation (1) and (2) to find the value of $q$.
$3q = 24$
$ \Rightarrow q = \dfrac{{24}}{3}$
On simplification we get,
$ \Rightarrow q = 8$
Now we substitute the value of $q = 4$ in equation (1) to find the value of the correct answer.
$p + 8 = 50$
Now, simplify the above equation as,
$ \Rightarrow p = 50 - 8$
Subtract the above numbers and we get,
$\therefore p = 42$

Therefore, the number of correct answers is $42$.

Note: As we know that to solve the unknown variables by using the equations we need the same number of equations as the unknown, that is if the number of unknown are two then we need at least two equations and as the number of unknown increases, the number of equations increases.