Math Teachers HELP!

Updated on October 22, 2012
S.E. asks from Landenberg, PA
5 answers

A mystery number is greater than 50 and less than 100. You can make exaclty five different rectangles with the mystery number of tiles. Its prime factorization consists of only one prime number. What is the number?

We've been at this a while. I just can't figure it out.

We think it might be 81 and the prime is 3 to the 4th power.... ??????????????

That is the entire question and it is not related to other questions on the page.

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So What Happened?

Thanks for that answer, but I'm not convinced it is right. t says only one prime factor so we were thinking the 3 x 3 x 3 x 3 worked better. They were just learning the concept of "to the x power".

Love teaching math, thank you, that's pretty much the way I figured it but it seemed kind of tricky for 5th grade.
Tough question. Anyone else want to chime in????

More Answers

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S.R.

answers from El Paso on

Okay. Based on the fact that the prime factorization consists of a single prime number used multiple times, you already have eliminated it down to either 2 to the 6th or 3 to the 4th, being either 64 or 81. Neither one of those is able to create 5 distinct rectangles, though. 64 can make 4, 81 only 3. So unless I'm missing something (always possible), this doesn't check out.... Let me do some looking.

ETA: Okay, here is the ONLY way I can get this to work. Using 3^4 with a mystery number of 81, you (by my view) only get 3 distinct rectangles. UNLESS, they are counting rectangles differently. IF they consider order making them unique, then you could have 5.

1x81
81x1
3x27
27x3
9x9

That is the ONLY way I can find to get 5 "different" rectangles, although to me, there are only 3. There's NO way to get 5 out of 64, so 81 seems like the best bet to me, but it's certainly not a good question.

5 moms found this helpful
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K.S.

answers from Minneapolis on

The problem with the answer in the link provided is that 2 is also a prime number.

Seems to me the answer would have to be 64 (2 x 2 x 2 x 2 x 2 x2)
As for the rectangles...hmm

1x64
2x32
4x16
8x8
??? not sure

1 mom found this helpful

J.E.

answers from Erie on

5th grade math?! I am in soooo much trouble 4 years from now lol.

I hope my kids are math geniuses b/c I will be no help :\

Smallavatar-fefd015f3e6a23a79637b7ec8e9ddaa6

B.G.

answers from Springfield on

I'm going to have to agree with LoveTeachingMath. 2^6=64 and 3^4=81, and neither of those numbers will give you 5 distinct rectangles.

The answer in the link below assumes two things that are not stated in your post:

1. Rectangles need to have an area that is an even number - not true. There are many rectangles with an odd area. So one of the factors is not necessarily 2.

2. The fact that the number can make 5 distinct rectangles does not mean that one of the factors is 5. That's using the same number in two different ways. 5 does not need to be one of the factors.

Was there any other information given in the problem?

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