Daily Scribe for 4/26/10

Today in class, we began to focus, among other things, upon mantaining an equivalent value between two things.
In other words, we were learning how to keep a balance.

We did a labsheet involving "gold coins" and "diplomatic pouches". The idea was that each pouch contained a certain number of gold coins. On one side, there was a certain amount of gold coins, and perhaps a pouch or two. On the other side was a diferent amonut of coins, and possibly pouches. By eliminating the same number of coins and pouches on each side, we were eventually able to come up with one pouch, and however many gold coins.


For pouches, I am going to use X's. For coins, I am going to use Y's.

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A) y y y y y y y y y y = x x x y y y y

10 y's = 3 x's plus 4 y's. First, you can eliminate 4 y's from each side. The new equation will be:

y y y y y y = x x x

So, 6 y's = 3 x's. This means 1 x = 2 y's.

Therefore, if x means pouches and y means coins, there are 2 coins per pouch.



B) x x x y y y = y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y

3 x's plus 3 y's = 30 y's, so you can eliminate 3 y's from each side.

x x x = y y y y y y y y y y y y y y y y y y y y y y y y y y y

3 x's = 27 y's, so 1 x = 9 y's. Therefore, there are 9 coins per pouch.



B2) x x y y y y = y y y y y y y y y y y y

2 x's and 4 y's = 12 y's. This means that 4 y's can be taken from each side.

x x = y y y y y y y y

2 x's = 8 y's. This means that 1 x = 4 y's. In other words, there are 4 coins per pouch.



B3) x x x = x x y y y y y y y y y y y y y

3 x's = 2 x's and 12 y's, so this time 2 x's can be eliminated from each side.

x = y y y y y y y y y y y y

x = 12 y's, so there are 12 coins per pouch.



B4) x x x y y y = x x y y y y y y y y y y y y

3 x's and 3 y's equals 2 x's and 12 y's. First take 2 x's away from each side.

x y y y = y y y y y y y y y y y y

1 x and 3 y's = 12 y's, so now 3 y's can be taken away from both sides as well.

x = y y y y y y y y y

x = 9 y's. Therefore, there are 9 coins per pouch.



B5) x x y y y y y y y y y y y y y y y y y y y y y = x x x x x y y y

2 x's and 21 y's = 5 x's and 3 y's. First take away 2 x's from each side.

y y y y y y y y y y y y y y y y y y y y y = x x x y y y

21 y's = 3 x's and 3 y's, so now eliminate 3 y's on each side.

y y y y y y y y y y y y y y y y y y = x x x

18 y's = 3 x's, so 6 y's = 1 x. There are 6 coins per pouch.

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That was a run-through of pretty much everything we covered in class today. Hopefully, you have now gained a clearer understanding of equivalent balances!

Signed,

Grace T :)