Suppose we have a bag with 10 slips of paper in it. Eight slips have a 3 on them and the other two have a 9 on them.
How many 9's do I have to add before the expected value is at least 8?
Write as equation:
\(3 \times 8 + 9 \times 2 + 9x = 8(10+x)\)
\(42+ 9x=80+8x\)
\(42+x=80\)
\(x =\color{brown}\boxed{ 38}\)