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