Final answer:
To find the number of bottles of mustard they went through, we need to determine the number of used bottles of ketchup. From there, we can use the given ratio to calculate the number of bottles of mustard.
Step-by-step explanation:
To find the number of bottles of mustard they went through, we can start by determining how many bottles of ketchup were used. If customers used half of the ketchup bottles, that means they used 1/2 of the total bottles. Let's say there were X bottles of ketchup in total, then the number of used bottles would be (1/2)X.
Now, we know that they used 35 times as much mustard as ketchup. So the number of bottles of mustard they used would be 35 times the number of used bottles of ketchup. Therefore, the number of bottles of mustard they went through is (35*((1/2)X)).