# Thread: Need help on word problem.

1. ## Need help on word problem.

Jan has a 18X18X12 inch gift box that needs to be placed carefully into a 2X2X2ft shipping carton, surrounded by packing peanuts.

a. How many 1-cubic-foot bags of peanuts does Jan need to buy?

b. Jan opens one bag of peanuts and spreads them evenly on the bottom of the shipping carton. What is the resulting depth of the peanuts?

c. Jan centers the square base of the gift box on the peanut layer,pours in another bag of peanuts, and spreads them evenly around. Now how deep are the peanuts?

d. Explain why the third bag of peanuts will cover the gift box.

Thanks.

Vicky.

2. Originally Posted by Vicky1997
Jan has a 18" X 18" X 12" inch gift box that needs to be placed carefully into a 2 ' X 2' X 2' shipping carton, surrounded by packing peanuts.

a. How many 1-cubic-foot bags of peanuts does Jan need to buy?
Hi Vicky1997,

Jan has a gift box that occupies a space of $1.5 \cdot 1.5 \cdot 1=2.25$ cubic feet.

The shipping container has $2 \cdot 2 \cdot 2 = 8$ cubic feet of space.

The difference between the shipping crate's volume and the gift box is $5.75$ cubic inches.

Looks like she'll need 6 bags if each bag contains 1 cubic foot and we're filling even with the top of the shipping box.

Originally Posted by Vicky1997
b. Jan opens one bag of peanuts and spreads them evenly on the bottom of the shipping carton. What is the resulting depth of the peanuts?
The base of the shipping crate is 2 feet by 2 feet. To find the height that one bag of 1 cu ft of peanuts would cover, we solve this:

$2 \cdot 2 \cdot h = 1$

So the peanut depth is $\frac{1}{4}$ foot or 3 inches.

Originally Posted by Vicky1997
c. Jan centers the square base of the gift box on the peanut layer,pours in another bag of peanuts, and spreads them evenly around. Now how deep are the peanuts?
Now if she places the square side down (1.5 by 1.5), we can determine that there will be $2 \cdot 2 - 1.5 \cdot 1.5=1.75$ square feet left around the gift box. So we do what we did before. We're dumping another 1 cubit feet of peanuts around the gift box. Solve this:

$1.75 \cdot h=1$ which is $\frac{4}{7}$ of a foot higher. Counting the other $\frac{1}{4}$ foot along with this we are now at $\frac{23}{28}$ feet deep or about 9.9 inches.

Originally Posted by Vicky1997
d. Explain why the third bag of peanuts will cover the gift box.
If she dumps another bag in, that will raise the height of the peanuts to another $\frac{4}{7}$ feet to make the depth now at $\frac{1}{4}+\frac{4}{7}+\frac{4}{7}=\frac{39}{28}$ or about 16.7 inches.

That is clearly over the top of the 12 inch gift box.

Now, this was a lot of arithmetic, and there may be errors. Check it over to see if it sounds logical to you. Maybe one of the other MHF helpers will check my work. Good luck.

3. Thank you soooooo much.

Vicky