# 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
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.

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.

### Relevant Questions

Grades in three tests in College Algebra are 87,59 and 73.
The final carries double weight.
The average after final is 75
The points needed on the final to average the points to 75 when the final carries double weight.
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The points needed on the final to avetage the points to 75.
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Grades in three tests in College Algebra are 87, 59 and 73.
The average after final is 75.
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