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# 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.

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