LCM(6,14) = 42, so the 42nd guest will receive both.
For the mints, 256 guests at 1/12 lb/guest shows she needs
256/12 = 21.33 lbs of mints
8 1/2 lbs only serves 102 guests (8*12 + 6)
For the mints, 256 guests at 1/12 lb/guest shows she needs
256/12 = 21.33 lbs of mints
8 1/2 lbs only serves 102 guests (8*12 + 6)
if you have to, just list em all out
Mugs: 6,12,18,24,30,36,42,48,54,60....
Shirts: 14,28,42,56,70....
See any numbers in common so far? Yep: the 42. So the 42nd guest will get both
Second one: Can't figure it out, cuz not enough information, did you leave something out, like how many place settings there are?
So if your prime factorize 6 and 14 you will get 3x2 for 6 and 7x2 for 14.
There is a set of 2's so you take one and cross out the other. Now take 3 and 7 since this is LCM we keep the remaining.
7x3x2=42
42th visit
To find the LCM, we can list the multiples of each number until we find a common multiple:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60...
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112...
From the lists above, we can see that 42 is the smallest number divisible by both 6 and 14. This means that the 42nd guest will be the first to receive both a mug and a t-shirt.
For the second question, let's calculate if Ellis will have enough mints:
She has 8 and 1/2 pound bags of mints, which is the same as 8 + 1/2 = 8.5 pounds.
She plans to put 1/12 pound of mints at each place setting.
To determine the number of place settings the 8.5 pounds will cover, we need to divide 8.5 by 1/12:
8.5 รท (1/12) = 8.5 ร (12/1) = 8.5 ร 12 = 102
Therefore, Ellis will have enough mints for 102 place settings.
I hope this helps! Let me know if you have any further questions.