To find out how much the student should score in the 6th subject to achieve an average of 74, let's solve it step by step:
1. Step 1: Understand the problem
The student has marks in five subjects and we need to find out the marks needed in the 6th subject to achieve an average of 74 across all six subjects. The marks in the five subjects are 80, 75, 62, 50, and 91.
2. Step 2: Calculate the total desired marks for an average of 74
We need to know the total marks that the student needs to have in all six subjects combined to have an average of 74.
The formula for the average is:
[tex]\[
\text{Average} = \frac{\text{Total Marks}}{\text{Number of Subjects}}
\][/tex]
Therefore,
[tex]\[
\text{Total Marks} = \text{Average} \times \text{Number of Subjects}
\][/tex]
Given the desired average is 74 and there are 6 subjects:
[tex]\[
\text{Total Marks Needed} = 74 \times 6 = 444
\][/tex]
3. Step 3: Calculate the sum of the marks obtained in the first five subjects
Add up the marks the student has already scored in the five subjects:
[tex]\[
80 + 75 + 62 + 50 + 91 = 358
\][/tex]
4. Step 4: Calculate the marks needed in the 6th subject
Subtract the sum of the first five subjects from the total marks needed to find out how much the student needs to score in the 6th subject:
[tex]\[
\text{Marks Needed in the 6th Subject} = \text{Total Marks Needed} - \text{Sum of Marks in First Five Subjects}
\][/tex]
Therefore:
[tex]\[
\text{Marks Needed in the 6th Subject} = 444 - 358 = 86
\][/tex]
The student needs to score 86 in the 6th subject to achieve an average of 74 across all six subjects.
