Friday, October 31, 2008

October 31, 2008

How many non-congruent right triangles with positive integer leg lengths have areas that are numerically equal to 3 times their perimeters?


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Wednesday, October 29, 2008

October 29, 2008

How many different combinations of $5 bills and $2 bills can be used to make a total of $17? Order does not matter in this problem.




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Tuesday, October 28, 2008

October 28, 2008

Casey's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will he need to do his job?




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Monday, October 27, 2008

October 27, 2008

A box contains gold coins. If the coins are equally divided among six people, four coins are left over. If the coins are equally divided among five people, three coins are left over. If the box holds the smallest number of coins that meets these two conditions, how many coins are left when equally divided among seven people?




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Friday, October 24, 2008

Thursday, October 23, 2008

October 23, 2008

Mr. Earl E. Bird leaves his house for work at exactly 8:00 A.M. every morning. When he averages 40 miles per hour, he arrives at his workplace three minutes late. When he averages 60 miles per hour, he arrives three minutes early. At what average speed, in miles per hour, should Mr. Bird drive to arrive at his work-place precisely on time?

Interactive version of problem and solution.



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Wednesday, October 22, 2008

October 22, 2008

Real numbers a and b satisfy the equations 3a = 81b + 2 and 125b = 5a – 3. What is ab?




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Tuesday, October 21, 2008

October 21, 2008

I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?






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Monday, October 20, 2008

October 20, 2008

Casey's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will he need to do his job?






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Friday, October 17, 2008

October 17, 2008

The equations 2x+7 = 3 and bx – 10 = –2 have the same solution. What is the value of b?

Interactive version of problem and solution.



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Thursday, October 16, 2008

October 16, 2008

Members of the Rockham Soccer League buy socks and T-shirts. Socks cost $4 per pair and each T-shirt costs $5 more than a pair of socks. Each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games. If the total cost is $2366, how many members are in the League?




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Wednesday, October 15, 2008

October 15, 2008

What is the value of (3x – 2)(4x + 1) – (3x – 2)4x + 1 when x = 4?

Interactive version of problem and solution.

Tuesday, October 14, 2008

October 14, 2008

The number 64 has the property that it is divisible by its units digit. How many whole numbers between 10 and 50 have this property?


Friday, October 10, 2008

October 10, 2008

A college student drove his compact car 120 miles home for the weekend and averaged 30 miles per gallon. On the return trip the student drove his parents' SUV and averaged only 20 miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip?

Interactive version of problem and solution.





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Thursday, October 9, 2008

October 9, 2008

The ratio of Mary's age to Alice's age is 3:5. Alice is 30 years old. How many years old is Mary?

Interactive version of problem and solution.



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Wednesday, October 8, 2008

Tuesday, October 7, 2008

October 7, 2008

Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grown half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now?

Interactive version of problem and solution.



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Monday, October 6, 2008

October 6, 2008

What is the minimum possible product of three different numbers of the set {–8; –6; –4; 0; 3; 5; 7}?


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Thursday, October 2, 2008

October 2, 2008

You and five friends need to raise $1500 in donations for a charity, dividing the fundraising equally. How many dollars will each of you need to raise?

Interactive version of problem and solution.

Wednesday, October 1, 2008

October 1, 2008

A player chooses one of the numbers 1 through 4. After the choice has been made, two regular four-sided (tetrahedral) dice are rolled, with the sides of the dice numbered 1 through 4. If the number chosen appears on the bottom of exactly one die after it is rolled, then the player wins $1. If the number chosen appears on the bottom of both of the dice, then the player wins $2. If the number chosen does not appear on the bottom of either of the dice, the player loses $1. What is the expected return to the player, in dollars, for one roll of the dice?

Interactive version of problem and solution.