Jose lost 120
50-120= -70
Ling lost 80
50-80= -30
Ling won because he had -30 while Jose had -70
For the last part, you have to find where
attains its maximum over
. We have

so that

with critical points at
such that





So either

or

where
is any integer. We get 8 solutions over the given interval with
from the first set of solutions,
from the set of solutions where
, and
from the set of solutions where
. They are approximately






Tom has 39 silver dollars. You can do this on your head. Jimmy has 32, and Tom 39.