SOLUTION: Richie's average on his math test was 64%. On the next test he had a mark of 76%, and this raised his overall average to 67%. When he wrote the next test after this his average imp

Question 1203583: Richie's average on his math test was 64%. On the next test he had a mark of 76%, and this raised his overall average to 67%. When he wrote the next test after this his average improved again by 1%. What mark did he get on the last test?
A) 68% B) 69% C) 70% D) 71% E) 72%
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

x% = score on the last test
n = number of math tests he has taken before the 76% and x% scores

(sum of test scores)/(number of tests) = average score
(sum of test scores)/n = 64
sum of test scores = 64n

64n+76 = updated sum after taking another test
(64n+76)/(n+1) = updated average
(64n+76)/(n+1) = 67
64n+76 = 67(n+1)
64n+76 = 67n+67
64n-67n = 67-76
-3n = -9
n = -9/(-3)
n = 3
Richie has taken 3 tests so far to get an average of 64%
The fourth test score is 76% which moves the average to 67%

The 5th test score is unknown, which we call x.
What we do know is that taking this 5th test will move the average to 68%

(64n+76+x)/5 = 68
(64*3+76+x)/5 = 68
(268+x)/5 = 68
268+x = 5*68
268+x = 340
x = 340-268
x = 72

Answer: 72%

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