Question

Dear Mitch, 

Now that Christmas is over and Hanukkah is almost over, could you post the answers to the first set of balance scale questions that went up on November 30^th?

Thank you,

Seth V.

Newark, NJ

Answer

Dear Seth V.,

Absolutely!

Here they are: 

First, the Christmas one:

Answer:

In order to balance Scale C, you would need to add 4 CHRISTMAS TREES to the 5 SNOWMEN. 

Why?

We can combine two facts: 

1)      Scale A with 1 Tree and 3 Snowmen on the left is balanced (=) with 2 Candy Canes on the right

2)      And Scale B, with its left side that's holding 2 Snowmen and 3 Trees is balanced with 3 Candy Canes.

 
Just like in math, if you know that 3 = 3

                                                And 2 = 2,

You can see that 2 + 3 = 2 + 3

(Don't forget that balanced is another way of saying "equals").

 

So, combining the left side of A with the left side of B,

And

combining the right side of A with the right side of B, we get:

4 Trees + 5 Snowmen = 5 Candy Canes.

And, just as you could if the scales were real (instead of mere drawings) you can turn this scale around in the air, and you would see that to balance 5 Candy Canes takes 5 Snowmen + 5 Trees.

 

So, to balance the 5 Candy Canes in scale C, as the question asks, we need to add 4 Trees to the 5 Snowmen.

Now, for the Hanukkah one:

All you have to do is substitute:

1 Dreidel for each Candy Cane,

1 Candle for each Snowman,

and

1 Present for each Christmas Tree! 

But in case you'd like to see that done, here goes:

Answer:

In order to balance Scale C, you would need to add 4 PRESENTS to the 5 Candles.

Why? 

We can combine two facts:

First,   Scale A with 1 Present and 3 Candles on the left is balanced (=) with 2 Dreidels on the right

 

......Second, Scale B, with its left side that's holding 2 Candles and 3 Presents is balanced with 3 Dreidels. 

Just like in math, if you know that 3 = 3

                                                And 2 = 2,

You can see that 2 + 3 = 2 + 3

(Don't forget that balanced is another way of saying "equals").

So, combining the left side of A with the left side of B,

And

combining the right side of A with the right side of B, we get:

4 Presents + 5 Candles = 5 Dreidels.

And, just as you could if the scales were real (instead of mere drawings) you can turn this scale around in the air, and you would see that to balance 5 Dreidels takes 5 Candles + 5 Presents.

So, to balance the 5 Dreidels in scale C, as the question asks, we need to add 4 Presents to the 5 Candles.

Hope that helps,

And Happy Holidays!

Mitch