Question 834608
For the tests with grades
84, 78, 64, and 88 each test has a weighting of 1.
The final has a weighting of 2.

set w1 = the first weight
w2 = the second weight
w3 = the third weight
and so forth.
set g1 = the first grade
g2 = the second grade
g3 = the third grade
and so forth.
We are looking for a weighted average.
((w1)(g1) + (w2)(g2) + ... )/(sum of weights)

In our situation, g1 = 84, g2 = 78, g3 = 64, g4 = 88 and
g5 = unknown ( This is the final. ).
w1 = 1 , w2 = 1, w3 = 1, w4 = 1, w5 = 2
For our problem we have

((1)(84) + (1)(78) + (1)(64) + (1)(88) + (2)(g5))/(sum of the weights)
{{{(84 + 78 + 64 + 88 + (2)(g5))/(1+1+1+1+2)}}}
{{{(84 + 78 + 64 + 88 + (2)(g5))/(6)}}}
{{{(314 + (2)(g5))/(6)}}}
To simplify use x in place of g5
{{{(314 + 2(x))/(6)}}}
Set this equal to 80.
{{{(314 + 2x)/(6)=80}}}
Multiply each side by 6
{{{(314 + 2x)=80*6}}}
{{{(314 + 2x)=480}}}
add -314 to each side
{{{2x=480-314}}}
{{{2x=166}}}
{{{x=83}}}
We need a grade of 83 on the final to obtain an average of 80 .