Tirzah has a lot of purses and handbags; in total she has 26 purses and 24 handbags. Half the purses and 1/4 the handbags are fake. If the rest are authentic, how many purses and handbags in total are genuine? Let's think first. Chain of thought:
26 / 2 = 13 of the purses are genuine. 24 / 4 = 6 of the handbags are fake. 24 - 6 = 18 of the handbags are genuine. There are 13 + 18 = 31 genuine purses and handbags.
Therefore, the answer is 31.