Question

Alice is playing checkers against a computer and has won 8 games out of the 12 she's played so far.

Alice must win the next consecutive games to reach a winning percentage of 80%. After that, losing
consecutive games
will bring her winning percentage down to 50%.

Answer 1

Explanation:

`(8+x)/(12+x) =(80)/(100) =(4)/(5) \\40+5x=48+4x\\5x-4x=48-40\\x=8`

so she wins next 8 consecutive games to reach winning percentage of 80%.

let she loses next y games to reach winning percentage of 50 %.

`(16)/(12+8+y) =(50)/(100) =(1)/(2) \\(16)/(20+y) =(1)/(2) \\32=20+y\\y=32-20=12y=12`

Hence she loses next 12 games to reach winning percentage of 50 %.