Question

Two thirds of a number added to 6 is equal to the number. What is this number?

Answer 1

Let's start by:

Let x = the unknown number

Answer 2

0k

Answer 3

Here's what we're looking at:

2/3 of a number added to 6 is the number

Answer 4

Let's translate that directly into math.

Answer 5

Do you remember what the word "of" means?

Answer 6

Divide

Answer 7

Not divide... the other one. :)

Answer 8

(on a side note, usually the word 'per' means divide)

Answer 9

multiply?

Answer 10

That's right - multiply! :)

Answer 11

2/3 of a number added to 6 is the number

So we can change the line above to:

(2/3) (a number) added to 6 is the number

Answer 12

Now, what did we decide we were going to call our unknown number?

Answer 13

x

Answer 14

That's right. Now, do you remember what the word "is" means?

Answer 15

"is" is the conjugation of the English verb "to be" for he/she/it or a noun/proper noun.

Answer 16

So far, we have:

(2/3) (x) added to 6 is (x)

Answer 17

Yes, but what does it mean in the language of mathematics?

Answer 18

I forgot :(

Answer 19

What it's equal to?

Answer 20

Exactly! Is means "="

Answer 21

So far, we have:

(2/3) (x) added to 6 = (x)

Answer 22

yes

Answer 23

Now, there's a little trick with the language here. If we have 2/3x added to 6, it would be translated like this:

6 + (2/3)(x) = (x)

Remember, if it is "added to" 6 that means we have the 6 first, and we added the 2/3x to it.

Answer 24

Does that make sense?

Answer 25

I believe so, yes.

Answer 26

So, our equation is:

6 + 2/3 x = x

Answer 27

mm hmm

Answer 28

So, what would we do to solve this?

\[6 + \frac{2}{3} x = x\]

Answer 29

uhm

Answer 30

Take away six and have 2/x = x + 6

Answer 31

Well, if we take away six, we would have:
\[\frac{2}{3} x = x-6\]

Answer 32

Although - instead of that...

\[6 + \frac{2}{3} x = x\]Recognize that we have a fraction here.

Answer 33

Let's clear the fraction by multiplying each piece by 3.

Answer 34

\[(3)6 + (3)\frac{2}{3} x =(3) x\]

Answer 35

From there:
\[18 + 2x = 3x\]

Answer 36

18 + 2 + 3z

Answer 37

Well, the variable would still be with the 2.

Answer 38

18+2z=3z

Answer 39

Yes, now what?

Answer 40

Cover one of 'em up! And you realize that x equals 6! :D

Answer 41

Not quite...

Answer 42

18+2z=3z
-2z -2z
18=z

Answer 43

Oh thanks

Answer 44

do you believe in god?

Answer 45

So the number we're looking for is 18. :)

You're welcome!!

Answer 46

Do you believe in God?

Answer 47

Does my medal depend on my answer to that question?

Answer 48

yup

Answer 49

My answer is 'no'