Question

The marks obtained by a student of class X in the first and the second unit tests are 35 and 21, respectively. Find the minimum marks he should get in the annual examination to have an average at least 30 marks.
A. $x \leqslant 34$
B. $x \geqslant 34$
C. $x > 34$
D. $x < 34$

Answer 1

Hint: According to the question given in the question we have to determine the minimum marks he should get in the annual examination to have an average at least 30 marks when the marks obtained by a student of class X in the first and the second unit tests are 35 and 21, respectively. So, first of all we have to let the number of marks obtained in the annual exam be $x$.
Now, as mentioned in the question that the average of exams should be at least 30 so, we have to determine the value of x for this condition.
Now, we have to find the average of the given data but before that we have to understand about the average as explained below:
Average: Average is the result that we get when we add two or more than two numbers together and then divide the total by the number of that numbers we added together basically to determine the average we just have to find the sum of all the given numbers and then we have to count the numbers that we have already added so that we can divided the added number with the total numbers we counted.
Now, we have to add all the numbers and then we have to divide it with the total number of data as mentioned above.

Complete step-by-step solution:
Step 1: First of all we have to let the number of marks obtained in the annual exam as mentioned in the solution hint. Hence,
The number of marks obtained in an annual exam = $x$
Step 2: Now, we have to determine the sum of all the data to find the average as mentioned in the solution hint. Hence,
$ \Rightarrow $Sum$ = 35 + 21 + x$
Step 3: Now, we have to determine the total number of data which we added as mentioned in the solution hint. Hence,
$ \Rightarrow n = 3$
Step 4: Now, as from the solution step 2 and step 3 we can determine the average for the given data as we have to add all the numbers and then we have to divide it with the total number of data as mentioned above. Hence,
$ \Rightarrow $Average:
$
\Rightarrow \dfrac{{35 + 21 + x}}{3} \geqslant 30 \\
\Rightarrow56 + x \geqslant 30 \times 3 \\
\Rightarrow 56 + x \geqslant 90 \\
\Rightarrow x \geqslant 90 - 56 \\
\Rightarrow x \geqslant 34
 $
Hence, we have determined the minimum marks he should get in the annual examination to have an average at least 30 marks when the marks obtained by a student of class X in the first and the second unit tests are 35 and 21, respectively is $x \geqslant 34$.

Therefore option (B) is correct.

Note: It is not possible to determine the average of a single number and to determine the average we need a minimum two numbers.
To determine the average we just have to find the sum of all the given numbers and then we have to count the numbers that we have already added so that we can divide the added number with the total numbers we counted.