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?
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Answers
Answer:
He got 72 Marks in the Last Test
Step-by-step explanation:
We assume the 64% average was the average of N tests.
The sum of the average of his Maths Test will be 64N
On the Next test he had a Mark of 76
That means the sum of Maths Test conducted is N+1 and sum of grades of all the Test is 64n + 76 ÷ N + 1 = 67
on Simplifying we get
64n +76 = 67(n+1)
64n + 76 = 67n + 67
76 - 67 = 67n - 64n
9 = 3n
N = 3
We can say that the Average of 64% is from 3 TESTS (N=3)
After 4 tests his average is 67%
After 5th Test his average improved by 1% = 67 % + 1% = 68%
Sum of the First 4 Test is = 67 x 4 = 268
With a percentage score of x on the fifth test,
the sum of the grades on the first 5 tests with average is 68%
268 + x / 5 = 68
268 + x = 68 x 5
268 + x = 340
x = 340 - 268
x = 72
From the given question the correct answer is:
He got 72 marks on last test.
solution.
We assume the 64% average was the average of N tests.
The sum of the average of his Maths Test will be 64N
On the Next test he had a Mark of 76
That means the sum of Maths Test conducted is N+1 and sum of grades of all the Test is 64n + 76 ÷ N + 1 = 67
on Simplifying we get
64n +76 = 67(n+1)
64n + 76 = 67n + 67
76 - 67 = 67n - 64n
9 = 3n
N = 3
We can say that the Average of 64% is from 3 TESTS (N=3)
After 4 tests his average is 67%
After 5th Test his average improved by 1% = 67 % + 1% = 68%
Sum of the First 4 Test is = 67 x 4 = 268
With a percentage score of x on the fifth test,
the sum of the grades on the first 5 tests with average is 68%
268 + x / 5 = 68
268 + x = 68 x 5
268 + x = 340
x = 340 - 268
x = 72
Hence, He got 72 marks in last test.