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.

Calculation:
Let the grade in the final test be x
Average of n numbers ${\displaystyle a_1+a_2+a_3+\dots +a_n}$ is given by ${\displaystyle A=\frac{a_1+a_2+a_3+\dots +a_n}{n}}$
Since the final carries double weight, it is considered as 2 numbers and the score is doubled,
i.e.,
${\displaystyle A=\frac{87+59+73+2x}{5}}$
Given average is 75
Therefore,
${\displaystyle 5=\frac{87+59+73+2x}{5}}$
Multiplying both sides by 5
${\displaystyle 75\cdot 5=\frac{87+59+73+2x}{5}\cdot 5}$
${\displaystyle 375=219+2x}$
Subtracting 219 from both the sides,
${\displaystyle 375—219=219+2x—219}$
${\displaystyle 156=2x}$
${\displaystyle 2x=156}$
Dividing both sides by 2,
${\displaystyle \frac{2x}{2}=\frac{156}{2}}$
${\displaystyle x=78}$
Therefore the score required in final test to get an average of 75 with double weight for final test is 78.