When the ratio is 1:1, either is 1/(1+1) = 1/2 the total.
We want h(x) = g(x) - f(x).
h(x) = -2x + 9 -(6x - 5)
h(x) = -2x + 9 -6x + 5
h(x) = -8x + 14
Her pay will be ....
... $2396 × (100% -15% -6.2% -1.45%) -$95
... = $2396 × 0.7735 - 95
... = $1758.31
You could do this with two weighings assuming its a two pan balance - (1) place three balls on each side - if they balance out then its the remaining three that has abnormal ball (2) out of that group, place one ball on each side - if balances it out, the abnormal ball is the remaining one.
If the weighing in step (1) does not balance out, grab the group of three balls that is light or heavy and repeat step (2) described above.
