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?

Question

Please help me to solve this one! Thanks a lot🙏

Answer 1

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

Answer 2

Thanks a lot, it helps me a lot🙏