Question

The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. What is the lowest score?

Answer 1

Hint:Assume that the lowest marks obtained by a student in the class is ‘$x$’ and highest marks be ‘$y$’. Form a linear equation according to the given data and substitute the value of highest marks in the formed equation to get the lowest marks.

Complete step-by-step answer:
Let us come to the question. It is given that the highest marks obtained by a student in her class is twice the lowest marks plus 7. Assume the highest marks to be ‘$y$’ and lowest marks to be ‘$x$’. Therefore, mathematically,
$y=2x+7..................(i)$
Now, it is given that the highest marks obtained in the class is 87. Therefore, substituting $y=87$ in equation (i), we get,
$\begin{align}
  & 87=2x+7 \\
 & 2x=87-7 \\
 & 2x=80 \\
 & x=\dfrac{80}{2} \\
 & x=40 \\
\end{align}$
Hence, the lowest marks obtained in the class is 40.

Note: It is important to note that one can solve this question by using one variable only. We have been provided with the value of highest marks in the question. So, there is no need to assume it to be ‘$y$’. But we have to assume the lowest marks as some variable to form the linear equation.