[Katz]

I know someone on here can help me with this. I am not in school but work at a school cafeteria and I have a problem that needs solved so here I go... I use a 24x16 in. cake pan... I need to be able to get at least 70 servings out of this cake I just baked. Now my question is this... I use to cut 2x2 in. pieces but that makes too many (96 to be exact). What size can I use now and get 70 pcs. Or no more than 75? Thanks for all your help.

[Remyth]

Cut the pieces into perfect 2.34'' squares or into just smaller than 2x3 pieces for 70 pieces. The math is 24x16=384, 384\70=5.486 sq. in. square root of 5.486=2.34''.

[Katz]

Cut the pieces into perfect 2.34'' squares or into just smaller than 2x3 pieces for 70 pieces. The math is 24x16=384, 384\70=5.486 sq. in. square root of 5.486=2.34''.

Well I was kind of on the right track. I got as far as 5.486 and then was lost. Thanks so much for your help Remyth. I am dumber than a box of rocks on sq. root stuff so your help is much appreciated. Thanks again Remyth :p

[Katz]

The math was right on and in my job this matters a lot.

[derobert]

To get 70 pieces, you need to cut enough rows and columns so the product (multiply them together) of those two is 70. There are several ways to make 70:

70 * 1 (duh)
35 * 2
14 * 5
10 * 7

Of those, I'd guess 10 x 7 is your best bet, with the long dimension cut into 10 and the short dimension cut into 7.

Both 71 and 73 are prime numbers, so it'd be difficult to cut that many pieces. 74 is hard too as its "almost" prime. There are a lot of things which multiple to 72, so that's a good one to use:

72 * 1
32 * 2
24 * 3
18 * 4
12 * 6
9 * 8

I'm guessing 9x8 would work OK, especially since 8 is easy to cut.

EDIT: Just to clarify, this is the number of pieces to cut in each direction, not the size of each piece. So 9x8 pieces would each be 24 in./9 pieces = 2⅔ in. by 16 in./8 pieces = 2 in. So the pieces would be 2⅔×2 in. The attached picture should explain

[Katz]

You my friend are a genius... thank you :)