I've been checking every day and now I'm wondering if I'm checking the wrong place. Did you post hints or answers to the Christmas and Hanukkah questions?
Las Vegas, Nevada
No, you did not miss anything. Two teachers wrote in that as soon as I post too much, the students go on their computers at home and 'get' the answer. So I held off, even though the Christmas math problem with the balancing scales is based on one of the most challenging algebraic questions most students ever see before high school.
First, the Hanukkah candle question.
To review, The 'HANUKKAH CANDLE QUESTION' asked how much it would cost a family if they followed the tradition of lighting two candles on the first night, three on the second, four on the third, etc., continuing the pattern for the full eight nights – IF -- the first night the two candles cost $2.00 (for the pair), and each night thereafter the family purchased candles that were 20% more expensive than the preceding night.
Rounding very slightly here and there, such as a penny up or a penny down when doing the 20% increases, we get:
Night 1: $2.00 for the 2 candles = $2.00
Night 2: $1.20 x 3 candles = $3.60
Night 3: $1.44 x 4 candles = $ 5.67
Night 4: $1.74 x 5 candles = $ 8.70
Night 5: $2.09 x 6 candles = $12.54
Night 6: $2.52 x 7 candles = $15.34
Night 7: $3.00 x 8 candles = $24.00
Night 8: $3.60 x 9 candles = $32.40
Total: = $104.25
Now, for the Christmas balancing scale question.
For younger grades, it is worth trying to make cards with each of the different items on them, one per card, but multiple copies of each card. Then, on freshly drawn balance scales, groups of students can try substituting cards on any side of any scale they can to keep the balance while narrowing in on the answer.
Also, HINT: The associative rule comes into play. (That says this: if a = b, and b = c, then a = c...)
And for older grades, think SYSTEMS OF EQUATIONS. AND ... What is the 'golden rule' regarding how many equations you need if you have four variables, or five? And what methods might one employ to get the number of equations and variables to work well together?
Answer coming soon.
Hope this helps,