Question

Suppose that x is a positive multiple of 3. If x cubed is less than 1000, what is the greatest possible value of x

Answer 1

Any ideas?

If x is a positive multiple of 3, then x can be described more specifically,
x = 3k, where k is a Natural Number.

Does that lead us anywhere?

Answer 2

it has to be a multiple of 3

Answer 3

I dont know

Answer 4

Do you see that "3k" IS a multiple of 3?

Answer 5

if think so

Answer 6

\(\dfrac{3k}{3} = k\) It IS a multiple of 3. Agreed?

Answer 7

yes

Answer 8

Now what? We have \(x^{3} < 1000\). What can we do with that?

Answer 9

find the higher multiple of 3 but less than 1000

Answer 10

You have reworded the problem statement. I'm glad we know what it is we are doing, but that doesn't get us anywhere.

We have \((3k)^{3} = x^{3} < 1000\)

What can we do with that?

Answer 11

I don't know

Answer 12

Consider expanding the left hand side.

Answer 13

I would start by asking what number x*x*x = 1000
any idea ?

Answer 14

Alternatively, we have \(x^{3} \lt 1000 \rightarrow x < 10\) Can you name the greatest multiple of three that is less than 10?

Answer 15

yes so we find greatest multiple of 3 but less than 7

Answer 16

*10 not 7

Answer 17

and that is 9

Answer 18

ok, and we know the number (I assume integer... they are not totally clear)
must be smaller. test 9
is that a multiple of 3 ?

Answer 19

yes

Answer 20

yeh i got it thanks

Answer 21

so 9 is the biggest number that is both a multiple of three and less than 10.
It's the answer

Answer 22

Sorry, I was messing with you a little. I SO want you to think in a way that you are not thinking. I forget that you are thinking the way you are thinking. :-( Anyway, you HAVE to find a way to proceed. "I don't know" just isn't good enough. If you're reading carefully, you now know another way to talk about multiples of 3. You must remember that Mathematics may require thinking that you are not used to. That's okay, but sometimes you have to treat it like a foreign language. You'll get it.