You want to copy a poster whose dimensions are 24 inches by 30 inches onto a piece of paper 5 inches by 11 inches. You want the image to be as large as possible, but maintain the proportions of the original poster



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1.

You want to copy a poster whose dimensions are 24 inches by 30 inches onto a piece of paper 8.5 inches by 11 inches. You want the image to be as large as possible, but maintain the proportions of the original poster. What scaling factor will you use?




2.

You want to copy a poster whose dimensions are 24 inches by 30 inches onto a piece of paper 8.5 inches by 11 inches. You want the image to be as large as possible, but maintain the proportions of the original poster. What are the dimensions of the image?




3.

You want to copy a poster whose dimensions are 24 inches by 30 inches onto a piece of paper 11 inches by 17 inches. You want the image to be as large as possible, but maintain the proportions of the original poster. What scaling factor will you use?




4.

You want to copy a poster whose dimensions are 24 inches by 30 inches onto a piece of paper 11 inches by 17 inches. You want the image to be as large as possible, but maintain the proportions of the original poster. What are the dimensions of the image?




5.

When comparing prices for pizzas, you discover that the large pizza has twice as much surface area of a medium pizza and costs less than two medium pizzas. However, your group decides to order two medium pizzas anyway. What additional factors could be omitted in the mathematical model?




6.

When comparing the relative dimensions of model trains you discover that their wheels are larger than they should be. Why might they be scaled incorrectly?




7.

The cost of photographic paper is nearly proportional to the area of the paper. But some shops charge extra for "nonstandard" sizes. Why would they feel the need to do this?




8.

Each year, the area's largest tomatoes and pumpkins are showcased at the county fair. If there is a maximum size for such produce, how can larger and larger specimens be grown each year?




9.

Other than the crushing strength considerations, what other factors limit the size of trees?




10.

How does a whale's size impact the depth to which it can descend?




11.

Are all rectangles similar? Why or why not?




12.

Are all circles similar? Why or why not?




13.

Are all pentagons similar? Why or why not?




14.

One of the famous problems of Greek antiquity was the duplication of the cube; that is, creating a cube similar to but double the volume of an existing cube. What if you instead wish to triplicate the cube, building a cube with three times the volume of an existing cube. What would be the scaling factor? Assuming the original cube was 1 cubic unit, what would be the dimensions of the larger cube?




15.

Create an example of an advertisement that misuses proportional change through its use of percent growth.




16.

Create an example of an advertisement that misuses proportional change through its use of graphics.




17.

Use the Consumer Price Index table to estimate when a loaf of bread, 50 cents in 1970, doubled in price.




18.

In 1997 a bottle of soda costs about 75 cents. Use the CPI table to estimate when this soda would have cost 5 cents.




19.

In the Consumer Price Index table, the index numbers tend to grow, but the numbers for the 1930s are less than those for the 1920s. Can you explain this?




20.

A miniature model for a sculpture weighs about 10 ounces and stands 8 inches high. The actual model is to be 3 feet high and weigh about 25 pounds. Can it be made from the same material as the model? If not, how should its weight per cubic inch compare to that of the model material?




21.

Why do spike heels cause more damage to hardwood floors than loafers?




22.

Large trucks often have multiple wheels on an axle. How would multiple wheels allow trucks to carry heavier loads?




23.

Why is allometric growth an appropriate model when the National Center for Missing and Exploited Children create sketches of missing people?




24.

Find the values of a and b so that the points (0.5, 21) and (1.4, 56) lie on the curve y = bxa.




25.

Find the values of a and b so that the points (1.1, 14) and (1.4, 38) lie on the curve y = bxa.




26.

A casino plans to redecorate its courtyard, and the plans include a large marble sculpture of a six-sided die. The sculpture will be 3 meters tall. The density of marble is 2700 kg/m3 and the crushing strength of marble is 7734 kg/m2. Find the pressure on the bottom face of the sculpture. What problem does your answer pose in regards to the feasibility of the sculpture?




27.

On a recent visit to the gym, Clark ran 3 kilometers and Bruce ran 3 miles. Who ran the farthest? How much farther (in kilometers) did he run?




28.

A scale model of a new building is being built for display. A scale of 1 cm to 3 m is being used. It took 27,000 square centimeters of cardboard to construct the exposed surfaces of the model. How much wood (in square meters) will be required to construct the surfaces of the building?




29.

Hisashi has a radio-controlled plane that is a scale model of a Boeing 727. The model has a 2-foot wingspan, and the wingspan of a Boeing 727 is 108 feet. If the minimum flight speed for a Boeing 727 is about 165 miles per hour, what is the minimum flight speed for the model plane?




30.

How many cubic centimeters are in 3 cubic meters?






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