Problem Solving

After 5 games, a rugby team had an average of 28 points per game. In order to increase the average by n points, how many points must be scored in a 6th game?
(A) n
(B) 6n
(C) 28n
(D) 28 + n
(E) 28 + 6n

I find B to be the right answer, but apparently the answer is shown as E. Please advice how this answer is arrived at.

Average of 5 games is 28. so, sum is 28*5

Let 'x' be the 6th game score.

(28*5 + x)/6 = 28 + n

28*5 + x = 28*6 + 6n

x = 28 + 6n

Let x be the points needed in the 6 th game .

Total points scored in 5 games = 28 x 5

So average of 6 games = [(28x5) + x ]/ 6

this average needs to be increased by n points = 28 (old average + n )

[(28x5) + x ]/ 6 = 28 + n

(28x5) + x = 6 (28 + n )

x = 28 (6-5) + 6n

x = 28 + 6n.

That is E.

Thanks