26/2=<<26/2=13>>13 of the purses are genuine.

24/4=<<24/4=6>>6 of the handbags are fake.

24-6=<<24-6=18>>18 of the handbags are genuine.

There are 13+18=<<13+18=31>>31 genuine purses and handbags

# Answer

31
<|im_start|>system
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<|im_start|>user
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?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
31
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?
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