Calculation:

Let the grade in the final test be x

Average of n numbers \(a_{1}+a_{2}+a_{3}+...a_{n}\ is\ given\ by\ A = \frac{a_{1}+a_{2}+a_{3}+...+a_{n}}{n}\)

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,

\(75 = \frac{87+59+73+2x}{5}\)

Multiplying both sides by 5

\(75*5 = \frac{87+59+73+2x}{5 * 5}\)

\(375 = 219 + 2x\) 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.

Let the grade in the final test be x

Average of n numbers \(a_{1}+a_{2}+a_{3}+...a_{n}\ is\ given\ by\ A = \frac{a_{1}+a_{2}+a_{3}+...+a_{n}}{n}\)

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,

\(75 = \frac{87+59+73+2x}{5}\)

Multiplying both sides by 5

\(75*5 = \frac{87+59+73+2x}{5 * 5}\)

\(375 = 219 + 2x\) 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.