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Question # To calculate: The points needed on the final to avetage the points to 75. Given information: Grades in three tests in College Algebra are 87, 59 and 73. The average after final is 75.

Upper level algebra
ANSWERED To calculate:
The points needed on the final to avetage the points to 75.
Given information:
Grades in three tests in College Algebra are 87, 59 and 73.
The average after final is 75. 2020-10-19
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 $$\displaystyle{A}={\frac{{{a}_{{{1}}}+{a}_{{{2}}}+{a}_{{{3}}}+\ldots+{a}_{{{n}}}}}{{{n}}}}$$
Plugging the values,
$$\displaystyle{A}={\frac{{{87}+{59}+{73}+{x}}}{{{4}}}}$$
Given average is 75
Therefore,
$$\displaystyle{75}={\frac{{{87}+{59}+{73}+{x}}}{{{4}}}}$$
Multiplying both sides by 4
$$\displaystyle{75}\cdot{4}={\frac{{{87}+{59}+{73}+{x}}}{{{4}}}}\cdot{4}$$
$$\displaystyle{300}={219}+{x}$$
Subtracting 219 from both the sides,
$$\displaystyle{300}—{219}={219}+{x}-{219}$$
$$\displaystyle{81}={x}$$
$$\displaystyle{x}={81}$$
Therefore the score required in final test to get an average of 75 is 81.