Diane flew home from vacation with a heavy bag. With the first airline she flew, Diane had to pay $14 to check her bag, plus $26 for every kilogram that her bag was over the weight limit. The next flight was with another airline that had the same weight limit. Diane had to pay $9 per kilogram that her bag was over the weight limit, in addition to the checked bag fee of $31. By coincidence, the fees ended up being the same with both airlines. Write a system of linear equations to represent the situation

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.