SOLUTION: Mrs. Nelson is on the refreshment committee for the annual school dance. She need to buy paper plates, napkins, and paper cups for the dance. The plates come in package of 24, the

Question 166505: Mrs. Nelson is on the refreshment committee for the annual school dance. She need to buy paper plates, napkins, and paper cups for the dance. The plates come in package of 24, the napkins in package of 20, and the paper cups in package of 16.
A. What is the least number of package she needs to buy in order to have the same number of each item? How many of each item will she have?
B. About 360 students have said that they will attend the dance. If Mrs. Nelson buys the number of items from part (a), will she have enough for one for each student? If not, how many more packages of each item will she need to buy? Will she have any item left over?
**Please help, I have been working at this problem all weekend**
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
What you are essentially doing here is finding the LCM (lowest common multiple) of 24, 20, and 16. Remember, the LCM is the SMALLEST number that two other whole numbers can go into. For instance, 15 is the LCM of 3 and 5 since both 3 and 5 can go into 15 evenly (and 15 is the smallest that 3 and 5 can go into)

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So let's find the LCM of 24, 20, and 16

First, list the prime factorization of each number. If you need help with prime factorization, check out this solver.

24: 2*2*2*3

20: 2*2*5

16: 2*2*2*2

Now highlight the unique factors. Remember, highlight the factors that occur most frequently

24: 2*2*2*3

20: 2*2*5

16: 2*2*2*2

Now multiply all of the highlighted factors

2*2*2*2*3*5=240

So the LCM of 24, 20, and 16 is 240

Note: there are many ways to find the LCM. Let me know if this method does not make sense to you.

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Now take the LCM and divide it by 24 to get the number of plate packages:

So she'll need to buy 10 plate packages to get 240 plates

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Now take the LCM and divide it by 20 to get the number of napkin packages:

So she'll need to buy 12 napkin packages to get 240 napkins

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Finally, take the LCM and divide it by 16 to get the number of paper cup packages:

So she'll need to buy 15 paper cup packages to get 240 paper cups

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Answer:

So she needs to buy 10 plate packages, 12 napkin packages, and 15 paper cup packages to get 240 plates, 240 napkins, and 240 cups.

# 2

Since there are 360 students and 360 is greater than 240 (the number of plates, napkins, and cups), this means that there won't be enough to go around.

So she'll have to buy another batch of 10 plate packages, 12 napkin packages, and 15 paper cup packages to get another 240 plates, 240 napkins, and 240 cups.

Now add the two batches to get
240+240=480

Since 480 is greater than 360, this means that she'll have enough (after she buys another batch of items)
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