Question

Dear Mitch,

Those balance scale problems you started putting up on your site have been a HUGE hit with my math classes, both the middle school classes and the high school classes.

Would it be possible for you to post one or two more of the holiday ones this week? I honestly don't think I can tell you how interested in the problem-solving aspect the students became, even some of the students I would never have imagined!

Thank you very much, and Happy Holidays to you and your family!

Mrs. B.,

Dearborn, MI

Answer

Dear Mrs. B.,

Absolutely!

We have been getting a tremendous response to these, so you are not alone!

Here now are two more balance scale problems. All you have to do is scroll down to the bottom of this response, and you will see one with a Christmas theme, and, following that, one with a Hanukkah theme!

(Though these two are entirely different from any that have been posted on this website before, the two that follow are very similar to each other, but of course we try to adapt these challenge problems to apply to a wider range of holidays than just one.)

Happy holidays,

And have fun with this!

Mitch

CHRISTMAS CHALLENGE PUZZLE:

There are three different kinds of Christmas decorations depicted in the following illustrations of balance scales. They are:

toy snowmen,

toy candy canes,

and

toy Christmas Trees.

Based on the fact that scales A and B are balanced perfectly, how many toy snowmen would you need to add to the right-hand side of scale C in order to form a balance with the left-hand side of that scale, which, as depicted in the illustration, is weighed down by two toy Christmas Trees and one toy candy cane?

For the second picture down, the one directly underneath the CHRISTMAS CHALLENGE PUZZLE, is the HANUKKAH CHALLENGE PUZZLE.

HANUKKAH CHALLENGE PUZZLE:

There are three different kinds of Hanukkah decorations depicted in the following illustrations of balance scales. They are:

toy Hanukkah presents

toy candles, and

toy dreidels (which are the holiday spinning tops that children use to play an ancient traditional game to have fun and win candy).

Based on the fact that scales A and B are balanced perfectly, how many toy Hanukkah presents would you need to add to the right-hand side of scale C in order to form a balance with the left-hand side of that scale, which, as depicted in the illustration, is weighed down by two toy dreidels and one toy candle?