How many test must i take in order to have a chance of scoring an average of 90% if I obtain 50% on my first test

Question

Help me to solve this please

Answer 1

That depends on what your scores are for the subsequent tests. If you score 50% on every subsequent test you'll never reach an average of 90%. If you assume that you'll score 100% on every test after the first, then using the equation for averages:

 

[50 + n*100]/(n+1) = 90

 

50 + 100n = 90n +90

 

10n = 40

 

n = 4

 

So if you assume you'll get 100% on every test after the first, you need to take 4 more to get an average of 90. 

Answer 2

There are several answers, depending on what you get on each test and how many tests you will have.

Suppose you get 98% on every test that you take from now on.

(50+98*x)/(x+1)=90

50+98x=90(x+1)

50+98x=90x+90

98x-90x=90-50

8x=40

x=5 tests of 98% will also do it

8 tests of 95% will do it but 8 tests seems like a lot of tests

also, there are variations of the 5 98% tests

96%, 97%, 98%, 99%, and 100% will do it as well

and, if you do have 8 more tests, there are many variations of these 8 tests

91%, 92%, 93%, 94%, 96%, 97%, 98%, and 99% will do it