Family Mathematics Problem Solving
Sponsored by
The Somerville Mathematics Fund

The Family Mathematics problems are written for adults and children to work on together. They are not meant as another homework to be turned in to your child’s teacher, instead it is an opportunity for you to work together to solve a mathematical problem. This Month’s Family Mathematics Problem is in the spirit of extravagant seasonal spending. We hope you will enjoy working together to solve these problems.

The Somerville Mathematics Fund was founded in 2000 to celebrate and encourage mathematics achievement in the city of Somerville. We offer scholarships to students and grants to teachers.
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From October 2003
 Solutions
  


Family Mathematics Problem Solving: Grades 4, 5, 6, 7, 8

The Twelve Days of Christmas
(1) How much would my true love need to spend to buy me all of these gifts according to these prices?
Listening to the song repeat and add items each time shows that we need to buy 12 of the first gift at $135, 11 of the 2nd gift at $15, and so to find the total cost:
(12 x $135) + (11 x $58) + (10 x $15) + (9 x $316) + (8 x $375) + (7 x $150) + (6 x $3,500) + (5 x $41.21) + (4 x $4,019.24) + (3 x $3,770.62) +(2 x $1,614.60) + (1 x $1,749.15) = $1,620 + $638 + $150 + $ 2,844 + $3,000 + $1,050 + $21,000 + $206.05 + $16,076.96 + $11,311.86 + $3,229.20 + $1,749.15 = $62,875.22
(2) If I was overwhelmed by the space that the number of gifts took up in my home and decided to return them, one each day starting the day after Christmas, on which date would I return the last gift?
Again, the first gift is given twelve times, the 2nd eleven times, and so the total number of gifts is:
(12 x 1) + (11 x 2) + (10 x 3) + (9 x 4) + (8 x 5) + (7 x 6) + (6 x 7) + (5 x 8) + (4 x 9) + (3 x 10) + (2 x 11) + (1 x 12) = 12 + 22 + 30 + 36 + 40 + 42 + 42 + 40 + 36 + 30 + 22 + 12 = 364 gifts. If I returned one gift per day, starting on the day after Christmas, I would finish on Christmas day 2003 (since 2003 is not a leap year).
(3) What is the percent inflation since 1985 for just one of each gift?
The cost of one of each gift is $15,743.82. That is an increase of $3,463.82 over the cost of $12,280 in 1985. To find the percent increase: divide 3,463.82 by 12,280 and multiply your quotient by 100. This gives an approximately 28% increase.