There were 14 board games
Let "v" be the number of video games
Let "b" be the number of board games
Given that The number of video games is 28 less than 6 times the number of board games
number of video games = 6 times the number of board games - 28
v = 6b - 28 ------ eqn 1
Also given that The games are 80% video games
So this means out of total games(video + board) , 80 % are video games
video games = 80 % of (video + board games)
v = 80 % of (v + b)
[tex]v = 80 \% \times (v + b)[/tex]
[tex]v = \frac{80}{100} \times (v + b)\\\\v = 0.8(v + b)\\\\v = 0.8v + 0.8b\\\\0.2v = 0.8b\\\\v = 4b[/tex]
Substitute v = 4b in eqn 1
4b = 6b - 28
-2b = -28
b = 14
Thus there were 14 board games
