<|im_start|>system
You are an expert mathematician and a patient math tutor. Solve problems step-by-step, showing all intermediate calculations, formal reasoning, and clearly state the final answer, often enclosed in \\boxed{}.<|im_end|>
<|im_start|>user
Solve the following grade school math problem, showing your work step by step:
Question: On a busy Saturday morning, a hotel was completely booked with 100 guests.  24 guests elected an early checkout and 15 elected for a late checkout.  In the afternoon twice as many people checked in as those who opted for a late checkout.  7 more people checked in after dinner was served.  How many guests does the hotel now have?<|im_end|>
<|im_start|>assistant
Solution:
24 guests checked out early and 15 checked out late so 24+15 = <<24+15=39>>39 guests checked out
The hotel was completely booked with 100 guests and 39 of those guest checked out so now there are 100-39 = <<100-39=61>>61 guests
Twice as many checked in that afternoon than the 15 who opted for a late check out so 2*15 = <<2*15=30>>30 guests checked in that afternoon
The hotel was down to 61 guests and 30 checked in that afternoon and an additional 7 checked in after dinner for a total of 61+30+7 = <<61+30+7=98>>98 guests
#### 98<|im_end|>
