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?

Speed

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

Scones

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.)

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.

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?

River Crossing

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

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?

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?