Ellis plans to hand out door prizes as the guest arrive she has 256 guests every 6th guest will receive a mug and for every 14 guests will receive a t shirt. Which guest will be the first to receive both mug and at shirt? Next question is elli has 8 and 1/2 pound bags of mints. She plans to put 1/12 pound at each place setting. will she have enough mints? PLEASE HELP I TRIED so hard and I can't get the answer thank you so much I need help with the answer before tomorrow morning!!!!!!!!!

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 first one:

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?

Yeah what Steve said

No she won't have enough

I agree with sam

You have to find the LCM=Least Common Multiple.

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

*42nd

You have to list the factors

So 42th person

To find out which guest will be the first to receive both a mug and a t-shirt, we need to find the least common multiple (LCM) of 6 and 14. The LCM represents the smallest number that is divisible by both 6 and 14.

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 ÷ (1/12) = 8.5 × (12/1) = 8.5 × 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.