Friday, December 31, 2010

Kidnappers' Demands

Your math teacher has been abducted by kidnappers who are demanding $20 million dollars in cash—twenty dollar bills with non-sequential serial numbers packed in a suitcase. A stack of 100 bills is about 1/2" thick and measures 25/8" by 63/16". A large suitcase can hold up to 6,000 cubic inches. Can you fill it with enough bills to meet the kidnappers' demands? If not, how many suitcases will you need? At 454 bills to a pound, how much will the $20 million weigh?

Currency Weight

The following table represents the value of currency currently in circulation in the United States. There are 454 notes in a pound of currency. Estimate the weight of paper currency currently in circulation.
Value in Circulation
$9.5 billion
$1.7 billion
$11 billion
$16.3 billion
$125.1 billion
$64.7 billion
$625 billion

Monday, December 20, 2010

Thursday, December 16, 2010

Russian Mathematicians Again

"Well," said Pavel. "I have two sons closer to one another in age than your two girls, though still some years apart. It is, perhaps, a coincidence that the product of their ages is exactly six times the sum."
"Ah," said Grigori. "Thank you for letting me know their ages."
How old are Pavel's sons?

Russian Mathematicians

Two Russian mathematicians, Pavel and Grigori met at a conference in Vienna where the following conversation ensued:
Pavel: Grigori! It's been such a long time. How are you?
Grigori: Fine, Pavel. And you? I hope you are well.
Pavel: Indeed, I am. It must be fifteen years. You have children now, I believe.
Grigori: Yes two darling girls.
Pavel: And how old are they?
Grigori: Well, it's curious. The product of their ages this year is just three times the sum.
Pavel: I'm sorry, Grigori, but I still can't work out their ages.
Grigori: Of course. I forgot to tell you how excited little Nikki was when Pavla was born.
Pavel then knew the ages of the two girls. What are they? How old was Nikki when Pavla was born?

Wednesday, December 15, 2010

Slope Point

A line with a slope of 2/3 passes through the point (3,7). What is the equation of the line?

Paying Bills

Rosa pays bills from her checking account. Her balance before paying bills is $632.74. She pays her energy bill for $237.29 and her water bill for $47.93. She also pays her telephone bill for $33.72. What is Rosa's checking balance after paying her bills?

Stopping Distance

At 35 mph a car has a stopping distance of about 50 feet. The stopping distance is directly proportional to the kinetic energy of the car, which is proportional to (mv2)/2, where m is the mass of the car and v is its velocity. How many more feet will be required to stop at 40 mph?

Kinetic Energy

A Ford Taurus with an 80-kg driver has a mass of approximately 1732 kg. The kinetic energy of the car and driver can be calculated from the formula E = (mv2)/2, where m is the mass of the car and driver, and v is the velocity. The resultant energy is expressed in joules (J). Find the kinetic energy of the car and driver at 27 m/sec.

Television Screen

This television is sold as a 32" screen because 32" is the length of the diagonals on the screen. The nominal ratio of the screen height to its width is 9:16. Using this information, calculate the height and width of the screen to the nearest 1/16th inch.

Paper Weight

A ream of bond paper consists of 500 sheets each 11" x 17". The weight of the paper refers to how much a ream weighs. For example, 24# paper weighs 24 pounds by the ream and is thicker and heavier than 20# paper. What is the nominal weight of a single sheet of 24# letter size (8.5" x 11") paper? Express your answer in ounces with 3 significant digits.

Saturday, December 11, 2010

Car Trip

Petra took a car trip. During the first 100 miles, she averaged 40 mph. During the next 100 miles, she averaged 50 mph. During the last 100 miles, she averaged 60 mph. What was her average speed for the whole 300-mile trip?

Overtime Pay

Carlos works at a job where he earns time and a half for any hours over 40 in the same calendar week or any hours over 8 in the same day. His base pay rate is $8.35 /hr. One week he works the schedule shown in the table. How much of his pay is for overtime?
Wednesay  9.5

Red Peppers

James buys 24 ounces of red bell peppers at $3.79 per pound. How much does he pay for the peppers?

Sum Product

The product of two integers is equal to their sum. What are the two integers? Prove that there are only two solutions.

Friday, December 10, 2010

River Crossing

Click the image to see it full size.

A surveyor made the measurements shown above to determine the distance x across the river. Find the value of x.

More Difference

The sum of two numbers is ten more than their difference. The difference is 7. What are the two numbers?

Gasoline Prices

Click the image to see it full-size.

Based on the graph above, which state has the highest average gasoline price? Which state the lowest? What is the percent increase from lowest to highest?

Thursday, December 9, 2010

Green Triangle

What is the area of the green triangle? How do you know?

Two Numbers

The product of two whole numbers is three times their sum, and their sum is twice their difference. What are the two numbers?

Wednesday, December 8, 2010


What is the circumference of the circle? Round your answer to two decimal places.

Fast Pitch

The fastest baseball pitch ever recorded in a major league game was made by Aroldis Chapman at PETCO Park in San Diego on September 24, 2010. His pitch was clocked by radar at 105.1 mph. The distance from the pitcher's mound to home plate is 60' 6". How long in milliseconds did it take the ball to travel from Chapman's hand to the strike zone over home plate?

Rhombus Area

Find the area of the rhombus depicted above.

Tuesday, December 7, 2010

Discounted Discount

Paul found a pair of trousers on the clearance rack discounted 80%. He also had a coupon that entitled him to an additional 15% off. He took the trousers to the checkout expecting to get 95% off. What mistake did Paul make? What was the actual discount Paul received?

Red Face

What is the probability of drawing a red face card from a randomly shuffled deck of standard poker cards?

Minnesota Voters

The Minnesota Secretary of State estimates that 3,799,328 Minnesotans were eligible to vote in a recent election. 55.46% of eligible voters cast ballots. About how many voters went to the polls? Round to four significant digits.

County Voters

For a recent election, there were 3,128,681 voters registered in Minnesota. Of those voters, 706,153 were registered in Hennepin County. What percent of voters were registered in Hennepin County? Round to the nearest whole percent.

Room Tiles

Heath plans to lay tile in a rectangular room measuring 10 feet by 11 feet. The tiles he plans to use are 8 inch square tiles. Any excess from tiles that require cutting will be discarded. How many tiles will Heath need to purchase for the room?

Fat Calories

A hamburger from a popular chain contains 670 calories and has 40 grams of fat. There are 9 calories in a gram of fat. What percent of the calories in the hamburger are from fat?

Dime Weight

A dime weighs 2/5 as much as a quarter. A quarter weighs 1/5 of an ounce. How many ounces does a dime weigh?

Quarter Pound

A roll of quarters weighs 8 ounces. There are 40 quarters in a roll. What is the monetary value of a pound of quarters?

Minnesota Population

The ratio of women to men in Minnesota is 251:249. There are 2,643,639 women in Minnesota. What is the total population of the state?

Room Size

A rectangular room has an area of 132 square feet. The sides of the room are in whole feet. What are the most likely length and width of the room?

Monthly Interest

Bridget borrowed $1,000 at 5% for 1 year. Her monthly payment is $85.61. How much of her first payment is interest?

Cheese Puffs

Tony made cheese puffs to take to a party. He put aside 1/7 of the puffs for his wife. He froze 1/3 of the puffs for later. He took ½ of the puffs to the party, and he ate all that remained. Tony did not break or crumble any cheese puffs. What is the minimum number of cheese puffs Tony could have made?


A five-foot post casts a shadow 4½ feet long. At the same time at tree casts a shadow 30 feet long. How tall is the tree?


A twenty-five foot ladder leans against a wall such that the top of the ladder is 24 feet from the ground. How far from the wall is the base of the ladder?

More Biscuits

A recipe for 21 biscuits calls for 2 cups of flour. How much more flour is needed to make 28 biscuits?

Comparing Fractions

Is 2/3 closer to ½ or ¾? Explain how you know.

Double Discount

Dagmar found a dress on the clearance rack for ¾ off the original retail price. She also had a coupon entitling her to an additional 15% off. The original price of the dress was $64. What was the price after discounts?

Milk Prices

From January 1 to February 1 the price of milk at the local grocery store increased from $2.89 per gallon to $3.29 per gallon. What was the percent of increase?

Baked Cookies

Gareth baked chocolate chip cookies. He set aside ½ of the cookies for his family. He put 1/3 of the remainder in a box to share with his co-workers. Then he took ¾ of the cookies that were still left to his neighbor. Finally he ate the remaining 3 cookies. How many cookies did Gareth make?

Peanut Butter

Bettina buys peanut butter at the local grocery story. A 40-ounce jar costs $4.29, and a 28-ounce jar costs $2.89. Which jar has the lower unit price? Explain how you know.

Driving Home

While Hector is driving home, he sees a sign that says his exit is ¾ mile ahead. He knows that the distance from the exit to his home is 2½ miles. How far from home is he when he sees the sign?

Stacking Boxes

Eloise stacks boxes on pallets in a warehouse. The maximum height of a pallet stacked with boxes is 58 inches. The pallet is 6 inches high. The boxes she has to stack are 82/3 inches tall. How many boxes high can she stack the pallet?