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Tammy is buying pens and pencils from the store. Pens come in packages of 10, but pencils are sold in packages of 12. If Tammy wishes to purchase the same number of pens as pencils, what is the smallest number of pens that she can buy?
pens
and pencils should have the same amount:
Let's call the number of pens "p" and the number of pencils "c".
We know that a package of pens has 10 pens, so the number of packages of pens Tammy buys can be represented as p/10.
Similarly, a package of pencils has 12 pencils, so the number of packages of pencils Tammy buys can be represented as c/12.
Since Tammy wants to buy the same number of pens as pencils, we can set p = c:
p/10 = c/12
p = (10/12)c
p = (5/6)c
Since we want the smallest number of pens Tammy can buy, we can assume that she should buy as few packages of pens as possible, which means rounding up the number of packages of pens she needs:
p = ceil((5/6)c)
For example, if Tammy wants to buy 24 pencils, she would need to buy:
p = ceil((5/6)24)
p = ceil(20)
p = 20
So Tammy would need to buy 20 pens (2 packages) and 24 pencils (2 packages).
wrong it is 60 =The least common multiple is the smallest whole number that is a multiple of each of two or more numbers.
solve
You need to find the smallest number that is a multiple of both 10 and 12. This is the least common multiple.
Write the prime factorization for each number.
10 = 2 × 5
12 = 2 × 2 × 3
Repeat each prime factor the most number of times it appears in any of the prime factorizations above.
The most the factor 2 appears is twice.
The most the factor 3 appears is once.
The most the factor 5 appears is once.
So, multiply:
2 × 2 × 3 × 5 = 60
The least common multiple of 10 and 12 is 60. That means that the smallest number of pens that Tammy can buy is 60, because 6 packages of 10 pens is 60 pens in total and 5 packages of 12 pencils is 60 pencils in total.
The smallest number of pens that Tammy can buy is 60.
Thank you for the correction! As an AI language model, I strive to provide the most accurate responses possible.
To find the smallest number of pens that Tammy can buy, considering that pens come in packages of 10 and pencils come in packages of 12, we need to find a common multiple of 10 and 12. The common multiple will represent the number of pens and pencils Tammy needs to buy in order to have the same quantity.
The multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
We can see that the smallest common multiple of 10 and 12 is 60. Therefore, Tammy needs to buy a minimum of 60 pens to have the same quantity of pencils.