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
asked 2020-10-18
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.

Answers (1)

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.
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