In 5 cricket innings sarah had an average of 45 runs per innings.
what should she score in her 6th innings to reach an average of 50?

Sarah you failure why are you playing cricket. 

But anyway, Sarah should score 75 runs in her sixth inning to reach an average of 50. To solve, first multiply 45 by 5 to reverse the division used to find her previous average. You should get 225. We want the score added to 225, the addend of them being divided by 6 to get 50, her average. Continue by putting your variables into an equation, then simplifying. Below, I distributed the division of the 6, then subtracted 37.5 from both sides of the equation, and finally multiplied both sides by 6 to get our final answer, a score of 75. 

(225 + x)/6 = 50 

37.5 + x/6 = 50  

x/6 = 12.5 

x = 75