Number Sense

On a recent drive, I happened to notice a sign indicating that for the next 4 miles the road would be descending at a 6% grade.  If we had been at 10,000 feet above sea level when I noticed the sign, how many feet above sea level will the car be when it reaches the end of the 4 miles?

Note: a 6% grade means that the road decends 6 feet for every 100 feet traveled.

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Measurement

The Board of Zoning requires that a 6" layer of gravel must be laid on all athletic fields before top soil is added to give adequate drainage.  Our gravel supplier says taht each truck load contains 12 cubic yards of gravel, at a cost of $9/25 per cubic yard delivered.

Calculate how many truckloads of gravel we should order for the soccer field and estimate how much it will cost.  Include your background calculations, your computations of the estimate, as well as the total cost for the project.

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Geometric Sense

I've got a triangle with sides of 3, 4, and 6.  What is the perimeter of the smallest triangle that is similar to the first one and has one side with length 12?

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Probability and Statistics

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Algebraic Sense

You've been asked to select a new tile pattern for your office.  You have found two patterns that you like and now must decide which to install.  The first pattern is dark green with light green triangles and comes in 3 inch by 3 inch squares, in boxes of 75.  Each box costs $55.21.  The second pattern is light green with dark green diamonds on it.  It comes in 9 inch by 9 inch squares, 12 to a box.  Each box costs $75.89.
 

Your office measures 15.5 feet by 12.25 feet, which means some tiles will have to be cut.  When you cut a tile, you may not use that tile again.

Since you can't decide on a pattern, you pick the least expensive one.  Which do you select?

In your answer, include the following data:

• total number of 3 inch tiles needed
• total cost of the 3 inch tiles
• total number of 9 inch tiles needed
• total cost of the 9 inch tiles

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Solves Problems and Reasons Logically

You have a job organizing a Ping Pong tournament for some of your fellow classmates.  Here is important information you need in order to organize the tournament.

• All matches are singles - one person plays against another person
• All players have to play all other players ONCE
• Individual matches take exactly one-half hour to play.
• Your school has only 4 ping pong tables available
• Six people register in advance for the competition

1.     If no other people register, how many games will be played in the tournament?
2.    Last year, nine people registered at the last minute.  If this happens this year, there will be a total of 15 people entered.  How many singles matches will have to be played?
3.    If you use all four tables, as often as possible, how long will the tournament last, given the original group of 6 entrants?

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Communicates Understanding

"Hoops" Malone has his contract up for renewal.  The team has offered him a choice of three contracts:

• $700,000 plus $5,000 for every game he plays
• $600,000 plus $10,000 for every game he plays
• $1,000,000 with a penalty of $25,000 for every game he misses

The season consists of 32 games.  Last season, "Hoops" only appeared in 12 gaems because of a knee injury.  If you were "Hoops" Malone, which contract would you pick?  Defend your decision.

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Makes Connections

Two couples are preparing for a summer trip from their home in Phildelphia to Rome, Italy.  Their plane leaves from Kennedy Airport in New York at 11:00 pm but they must check in three hours prior to departure.  Their problem is how to get from their home to the airport in New York, a distance of 120 miles.

They are considering two options - renting a car, or using a limousine service.  Here is what they have found out:
 

• Car Rental:
  • Flat rate of $78.00 each way
  • Insurance (optional) $14.95 each way
  • Tolls $8.00 each way
  • Free unlimited mileage, but the gas tank must be ful when the car is returned
• Limousine Service
  • Flat rate of $25 per person each way
  • A gratuity of 15% is expected
  • Departure schedule:
    Leave Phil 8:00 am - arrive NY 11:00 am
    Leave Phil 2:00 pm - arrive NY 5:00 pm
    Leave Phil 5:00 pm - arrive NY 8:30 pm

If you were making the trip, which option would you choose?  Defend your decision.

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