© Friederike Hofmann, MATH+
Challenge
Christmas is coming close again, so the elves are busy preparing all the presents! Due to the enormous number of presents, the elves start delivering presents three weeks in advance. That is, this year, they will be delivering during the weeks of December 2-8 (week 1), December 9-15 (week 2), and December 16-22 (week 3). The closer to Christmas, the more presents they deliver per week. However, not every day the same amount of presents is delivered. There are red and green gifts. The ratio between red and green gifts depends only on the day of the week and is the same throughout the three-week period.
To plan when each of the elves needs to work, the head elf wants to predict the number of deliveries per day. He has data on the number of presents of last year, which is given in Table 1 (given below). Luckily, humans are creatures of habit, so the present delivery number for this year will abide the following two rules:
- The deviation of the number of presents delivered on a day of the week from the average number of presents delivered during that week is the same as last year. For example, if on average three presents are delivered and on Monday one present is delivered, than the deviation for Monday from the average of that week is -2.
- The fraction of red presents delivered on a day of the week (with respect to the total number of presents delivered on that day) will be the same as last year. For example, if on Monday there were one red and two green presents delivered, then the fraction of red presents on Monday of that week is 1/3.
Table 1 shows the number of delivered gifts for week 1 (columns 3 and 4), week 2 (columns 6 and 7), and week 3 (columns 9 and 10).
For example, in this Table we can observe
- on each of the three weeks, Tuesday had 2 more presents delivered than Monday,
- on each of the three Mondays, half of the delivered presents were red, while on each Friday only one third was red,
- in week 1 there was a total number of 42 delivered presents and in week 2 the total number was 84.
One thing has changed this year: Christmas become more popular! Thus, the head elf knows that this year the total number of presents per week triples every week during the delivery weeks. Moreover, he knows that on Monday in week 1 (December 2) the elves will need to deliver 8 red and 8 green presents.
Question: How many red and green presents are there to be delivered on Saturday in week 3 (December 21)?
Possible Answers
1. 56 red gifts and 28 green gifts
2. 108 red gifts and 108 green gifts
3. 108 red gifts and 36 green gifts
4. 84 red gifts and 21 green gifts
5. 72 red gifts and 26 green gifts
6. 90 red gifts and 18 green gifts
7. 106 red gifts and 53 green gifts
8. 108 red gifts and 54 green gifts
9. 56 red gifts and 56 green gifts
10. 30 red gifts and 15 green gifts
Latest PDF Update: December 16, 10:20 am
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