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: To receive grade ‘$A$’ in the course, one must obtain an average of $90$ marks or more in five examinations (each of $100$ marks). Sunita's marks in the first four examinations are $87,92,94$ and $95$. Find minimum marks that Sunita must obtain in the fifth examination to get grade ‘$A$’ in the course.

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Last updated date: 29th May 2024
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Answer
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Hint: To get minimum marks that is necessary to obtain in fifth examination to get grade ‘$A$’ in the course, first of all we will find the minimum total marks are required for getting grade ‘$A$’ in the course by using the formula of average that is $\text{sum of all the marks required in the examination}=\text{total number of examinations}\times \text{average marks}$. Then, we will calculate the total of marks of four examinations obtained by Sunita. After that we will subtract total marks obtained by Sunita from the total minimum marks required to get grade$A$’ in the course.

Complete step by step answer:
Since, the given information in the question is:
Average marks $=90$
Total number of examinations $=5$
Now, we will use the formula to get the minimum total marks are required for getting grade ‘$A$’ in the course as:
$\Rightarrow \text{sum of all the marks required in the examination}=\text{total number of examinations}\times \text{average marks}$
Here, we will substitute the respective values in the formula as:
$\Rightarrow \text{sum of all the marks required in the examination}=\text{5}\times \text{90}$
After multiplication of $5$ and $90$ , we will get $450$ as:
$\Rightarrow \text{sum of all the marks required in the examination}=450$
Thus, the minimum total marks required for getting grade ‘$A$’ in the course is $450$.
Now, we will calculate the obtained marks of Sunita in four examinations as:
Total marks of Sunita in four exams $=87+92+94+95$
After doing addition all the numbers of above step, we will have:
Total marks of Sunita in four exams $=368$
Since, we have the minimum total marks required for getting grade ‘$A$’ in the course and the total marks obtained by Sunita in four exams. So, the required minimum marks that Sunita must obtain in fifth examination to get grade ‘$A$’ in the course can be calculated as:
$=450-368$
Now, we will have $82$ after subtraction as:
The required minimum marks that Sunita must obtain in fifth examination to get grade ‘$A$’ in the course can be calculated $=82$
Hence, the answer will be $82$ for getting the minimum marks that Sunita must obtain in the fifth examination to get grade ‘$A$’ in the course.

Note: Now, we can check whether the solution is correct or not by using obtained marks from the solution if the sum of Sunita’s marks for five examinations is equal to the required minimum marks to get grade ‘$A$’ in the course.
Total of Sunita’s marks of four examinations is $368$ and minimum marks for fifth exam is $82$. Now, the total of marks obtained by Sunita in all five examinations is:
$\begin{align}
  & =368+82 \\
 & =450 \\
\end{align}$
This is required minimum marks to get grade ‘$A$’ in the course. Hence, the solution is correct.