Miss Jennifer is buying pencils in packs of 12, notebooks in packs of 16, and red pens in boxes of 20. She needs to have the same number of pencils, notebooks, and red pens. What is the smallest number of packs of each type that she should buy?
Answer:
Miss Jennifer needs to buy
packs of pencils,
packs of notebooks and
packs of red pens.
We first need to find the LCM of 12, 16, 20. The answer is 240.
Then, we have to find out:
Pencils: 12*p=240. p=20
Notebooks: 16*n=240 n=15
red pens: 20*r=240 r=12
So that means that there are 20 pencils, 15 notebooks, and 12 packs of red pens. Hope this helped you!
20 pencils 15 notebooks 12 packs of red pens
Well, Miss Jennifer must be quite the organized person if she wants everything to be equal! Let's see how we can make that happen.
We want the smallest number of packs for each type, which means we need to find the least common multiple of 12, 16, and 20. Now, I'm no math whiz, but I think I can handle this.
The prime factors of 12 are 2, 2, and 3.
The prime factors of 16 are 2, 2, 2, and 2.
The prime factors of 20 are 2, 2, and 5.
To find the least common multiple, we need to take the highest power of each prime factor that appears in any of the numbers. So, we'll need four 2's, one 3, and one 5.
That means Miss Jennifer should buy 4 packs of pencils, 1 pack of notebooks, and 1 pack of red pens.
Oh, and while we're at it, maybe she should consider buying a pack of jokes too! Gotta keep the humor level up while shopping for school supplies, right?
To find the smallest number of packs of each type that Miss Jennifer should buy, we need to find the least common multiple (LCM) of 12, 16, and 20. The LCM is the smallest positive integer that is divisible by all three numbers.
To find the LCM, we can start by listing the multiples of each number until we find a common multiple:
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, ...
Multiples of 20: 20, 40, 60, 80, 100, 120, ...
From the lists above, we can see that the first common multiple for all three numbers is 48. So, Miss Jennifer needs to buy at least 48 pencils, 48 notebooks, and 48 red pens.
To determine the number of packs for each type, we divide the total number needed by the quantity in each pack:
Packs of pencils: 48 pencils ÷ 12 pencils per pack = 4 packs
Packs of notebooks: 48 notebooks ÷ 16 notebooks per pack = 3 packs
Packs of red pens: 48 red pens ÷ 20 red pens per box = 3 boxes
Therefore, the smallest number of packs Miss Jennifer should buy is 4 packs of pencils, 3 packs of notebooks, and 3 boxes of red pens.