What must your average be on the next 5 quizzes to increase your average to 81 out of 100?

Question

Suppose your average, after taking 3 quizzes, is 76 (out of 100). What must your average be on the next 5 quizzes to increase your average to 81 out of 100?

Answer 1

using algebra...

(3*76+5*x)/8=81

(3*76+5*x)=648

228+5x=648

5x=648-228

5x=420

x=420/5=84

using arithmetic...

each of the 3 76s is 5 short of 81 which means you need to make up for the lack of 15 points

you need 5 81s plus the extra 15 points

you need 81, 81, 81, 81, 81 plus 15 extra points so each 81 must be increased by 15/5=3 points

you need to get 84, 84, 84, 84, 84 just like the first time