To calculate: The points needed on the final to average the points to 75 when the final carries double weight. Given information: Grades in three teste in College Algebra are 87,59 and 73. The final carries double weight. The average after final is 75.

To calculate: The points needed on the final to average the points to 75 when the final carries double weight. Given information: Grades in three teste in College Algebra are 87,59 and 73. The final carries double weight. The average after final is 75.

Question
Upper level algebra
asked 2020-10-21
To calculate:
The points needed on the final to average the points to 75 when the final carries double weight.
Given information:
Grades in three teste in College Algebra are 87,59 and 73.
The final carries double weight.
The average after final is 75.

Answers (1)

2020-10-22
Calculation:
Let the grade in the final test be x
Average of n numbers \(\displaystyle{a}_{{{1}}}+{a}_{{{2}}}+{a}_{{{3}}}+\ldots+{a}_{{{n}}}\) is given by \(\displaystyle{A}={\frac{{{a}_{{{1}}}+{a}_{{{2}}}+{a}_{{{3}}}+\ldots+{a}_{{{n}}}}}{{{n}}}}\)
Since the final carries double weight, it is considered as 2 numbers and the score is doubled,
i.e.,
\(\displaystyle{A}={\frac{{{87}+{59}+{73}+{2}{x}}}{{{5}}}}\)
Given average is 75
Therefore,
\(\displaystyle{5}={\frac{{{87}+{59}+{73}+{2}{x}}}{{{5}}}}\)
Multiplying both sides by 5
\(\displaystyle{75}\cdot{5}={\frac{{{87}+{59}+{73}+{2}{x}}}{{{5}}}}\cdot{5}\)
\(\displaystyle{375}={219}+{2}{x}\)
Subtracting 219 from both the sides,
\(\displaystyle{375}—{219}={219}+{2}{x}—{219}\)
\(\displaystyle{156}={2}{x}\)
\(\displaystyle{2}{x}={156}\)
Dividing both sides by 2,
\(\displaystyle{\frac{{{2}{x}}}{{{2}}}}={\frac{{{156}}}{{{2}}}}\)
\(\displaystyle{x}={78}\)
Therefore the score required in final test to get an average of 75 with double weight for final test is 78.
0

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