The average scores of the last four tests taken by Mike is 86 marks. To raise the scores to 92 marks, at least how many times does Mike have to get 100 marks in a row?
Please help me to solve this one! Thanks a lot🙏
The average scores of the last four tests taken by Mike is 86 marks mean:
( x1 + x2 + x3 + x4 ) / 4 = 86
multiply moth sides by 4
x1 + x2 + x3 + x4 = 86 ∙ 4
x1 + x2 + x3 + x4 = 344
Mike have total 344 marks
When x times Mike get 100 marks awerage will be:
( 344 + x ∙ 100 ) / ( 4 + x ) = 92
multiply moth sides by 4 + x
344 + 100 x = 92 ∙ ( 4 + x )
344 + 100 x = 92 ∙ 4 + 92 ∙ x
344 + 100 x = 368 + 92 x
Subtract 92 x from both sides
344 + 100 x - 92 x = 368 + 92 x - 92 x
344 + 8 x = 368
Subtract 344 from both sides
344 + 8 x - 344 = 368 - 344
8 x = 24
x = 24 / 8 = 3
Proof:
The average scores after 4 + x = 4 + 3 = 7 tests will be:
( x1 + x2 + x3 + x4 + 100 + 100 + 100 ) / 7 =
( 344 + 300 ) / 7 = 644 / 7 = 92
Thanks a lot, it helps me a lot🙏
To solve this problem, we need to determine how many times Mike needs to score 100 in a row in order to raise his average score from 86 marks to 92 marks.
First, let's find the total marks Mike currently has for the last four tests. If the average of four tests is 86, then the sum of these four scores would be 86 multiplied by 4, which equals 344 marks (86 * 4 = 344).
Now, let's calculate the total marks Mike needs to have in order to achieve an average of 92. Since there will be a total of five tests (including the four previous tests and the future test where Mike gets 100 marks), the sum of these five scores should be 92 multiplied by 5, which equals 460 marks (92 * 5 = 460).
To determine the marks Mike needs to score in the future test, we can subtract the total marks he currently has from the total marks he needs to achieve the desired average. Therefore, 460 - 344 equals 116 marks (460 - 344 = 116).
Since each of Mike's scores can only be an integer value, we need to find the least number of times he must score 100 marks in a row to reach or exceed the required 116 marks.
To calculate this, we divide 116 by 100, and round up the result to the nearest whole number. So, 116 ÷ 100 equals 1.16. Rounding up, we find that at least 2 times are needed for Mike to score 100 marks in a row to raise his average scores to 92 marks.
Therefore, to achieve an average of 92 marks, Mike needs to get 100 marks on at least 2 consecutive tests.