Question

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 the minimum marks that Sunita must obtain in the fifth examination to get grade ‘A’ in the course?

Answer 1

Hint: We start solving the problem by recalling the definition of average of any given n terms. We then assign the variable for the marks in the fifth subject. Now, we use the definition of average of n terms to get the average of 5 examinations which is equal to 90. We then make necessary calculations to get the minimum marks required to obtain a final examination.

Complete step by step answer:
According to the problem, we have given that the average of 90 marks or more in five examinations is required to receive an ‘A’ grade. We need to find the minimum marks that Sunita must obtain in the fifth examination to get an ‘A’ grade if she already got 87, 92, 94 and 95 in the first four examinations.
We know that the average of ‘n’ terms ${{x}_{1}}$, ${{x}_{2}}$,……, ${{x}_{n}}$ is defined as $\dfrac{{{x}_{1}}+{{x}_{2}}+.....+{{x}_{n}}}{n}$.
Let us assume the marks in final examination be y. So, we need an average of 87, 92, 94, 95 and y at least 90 in order to receive an ‘A’ grade.
So, we have $\dfrac{87+92+94+95+y}{5}=90$.
$\Rightarrow \dfrac{368+y}{5}=90$.
$\Rightarrow 368+y=5\times 90$.
$\Rightarrow 368+y=450$.
$\Rightarrow y=450-368$.
$\Rightarrow y=82$.
So, we have found that Sunita must score at least 82 marks to receive an ‘A’ grade.
The minimum marks that Sunita must obtain in the fifth examination to get grade ‘A’ in the course is 82.
Note:
We said that 82 is the minimum mark required to obtain an ‘A’ grade. Because of increasing the marking in final examinations, the sum of the total marks increases which increases the average of 5 examinations. We should not make calculation errors while doing these problems. Whenever we are asked to do this type of problem, we should start solving by assigning the variables to the unknowns required.