Friday, May 31, 2013

Aspect ratio

Movies and the screens we view them on typically come in two formats. Standard format has a 3:4 aspect ratio, meaning that the picture height is 3/4 of the picture width. Widescreen format has a 9:16 aspect ratio, so the picture height is 9/16 of the picture width. A widescreen movie shown on a standard screen has two horizontal black bars, one above and one below the picture. Likewise, a standard movie shown on a widescreen screen has vertical black bars on the sides. What percent of the viewing area is lost to the black bars when viewing a widescreen movie on a standard screen? How about when viewing a standard movie on a widescreen screen?

Friday, May 10, 2013

Perimeter is Area

A rectangle is 3 inches longer than it is wide. The value of it's perimeter in inches is the same as the value of its area in square inches. What is the width of the rectangle?

Thursday, November 29, 2012


You are in your car going 5 miles in 4 minutes. What is your speed in miles per hour?

Friday, November 16, 2012


A recipe for scones calls for 3 cups of flour and 10 tablespoons of butter and makes 12 scones. You only have 2 cups of flour, but you can still make 8 scones. How much butter should you use? (Hint: 1 tablespoon = 3 teaspoons.)

Thursday, November 15, 2012

Find a Line

Find the equation of a line that passes through −3 on the y axis and 2 on the x axis.

Wednesday, November 14, 2012

Coin Stacks II

It is possible to mix coins in a stack to get a stack a whole number of millimeters high. For example, a stack of 2 nickels and 2 pennies has a height of exactly 2 × 1.95 + 2 × 1.55 = 7 mm. Can you find a stack of coins with a whole number of millimeters less than 7?

Coin Stacks

US coins have different thicknesses as specified below:
Penny 1.55 mm
Nickel 1.95 mm
Dime 1.35 mm
Quarter 1.75 mm
Two stacks of coins may have the same height but a different number of coins. For example, a stack of 39 pennies has a height of 39 × 1.55 = 60.45 mm, and a stack of 31 nickels also has a height of 31 × 1.95 = 60.45 mm. Find the smallest number of dimes and quarters that can likewise be made into two stacks the same height.