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 Problems are about large numbers and money. We hope you will enjoy working together to solve these problems. Link to the solution is below.
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 September 2002
 Solutions
  
Grades 4, 5, 6, 7, 8
Grades 6, 7, 8


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

Money, Money, Money.... Lots of Dollars
Tom Brady should either figure out how high $4,000,000 would be if it were stacked up or figure out how many bills would be in a mile high pile.
If he chose to figure out the height of four million dollars and it was less than 5,280 feet, then he would need to calculate how many dollars would be in a mile-high pile. So, starting with the mile-high pile is more efficient.
There are 5280 x 12 inches = 63,360 inches in a mile.
Each bill is .0043 inches thick.
63,360 / .0043 = $14,734,884 in a mile-high pile of one-dollar bills.
The mile high pile is definitely a better deal. By the way, $4,000,000 is 17,200 inches tall--so going with the mile high pile gives him more than three and a half times as much money!

Family Mathematics Problem Solving: Grade 6, 7, and 8
Tom Brady needs to get his bonus home. The volume of the box must hold:
14,734,884 x 6.14 x 2.61 x .0043 = 1,015,369 cubic inches.
There are 1728 cubic inches in a cubic foot, so the box would need to hold 1,015,369 / 1728 = 588 cubic feet.
There are various dimensions of the box, it is important that the length is a multiple of 6.14 inches and the width is a multiple of 2.61 inches so that the bills can be stacked neatly into the box.
Can Tom Brady lift the box? As a professional athlete he is strong, but is he strong enough?
If he insists on only new bills (they weigh less) then
14,734,884 / 1000 x 2.2 = 32,417 pounds --- more than sixteen tons!
 


Other Problem Solving Sources:
http://mathforum.org/pow/
http://www.figurethis.org/index40.htm
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