WP4a
Practice - The Equal Ratios Method
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. A movie is open from noon to 11:30 pm. If a complete showing of a movie takes 2 hours and 15 minutes, how many complete showings can the movie run in a day?
2. You have a scale model of a prism. The length of the model prism is 50 cm. Each centimeter of the model represents 2 meters of the actual prism. What is the ratio of the area of the base of the model to the area of the base of the actual prism?
3. A tree has been growing at a rate of 5 feet every three years. What is its annual rate of growth?
4. Mike walks a half mile in 12 minutes. How many miles can he walk in 3 hours?
5. Your recipe calls for 3/5 of a cup of flour to make a batch of biscuits. How many batches could you make with 7 cups of flour?
6. You drive 342 miles on 12 gallons of gas. What is your average miles/gallon?
7. Your baseball team has won 5 out of 8 games. At the same rate, how many games will you have to play to win 40 games?
8. The scale on a map says 1/4 inch equals 20 miles. How many miles would be represented by 3.5 inches?
9. You read 300 pages in 12 hours. How long does it take you to read 400 pages?
10. John rides a bike to work. He rides 10 miles at 15 miles/hour. Jim walks to work. He walks 2 miles at 3 miles/hour. If they leave at the same time, does John arrive (first, second, or at the same time as Jim)?
11. You and your friend work on a job. You work three times as many hours as he does. The two of you are paid $800. You work at the same hourly rate. How much money do you get?
ANSWERS
1. If a single showing takes 2-1/4 hours, then 2-1/4 divided by 1 equals 11-1/2 divided by x. So 2-1/4 times x = 11-1/2, and x = 11.5/ 2.25, and x= 5.11. Five showings.
2. The ratio of the model prism's length to the actual prism's length is 50 cm./2 m. Since there are 100 centimeters in a meter, the ratio is 0.5 m. / 2 m., or ¼. So the ratio of the areas would be (¼)², or 1/16.
3. Set up the ratios (5/3) = (x/1). Then cross-miltiply: 3x = 5, so x = 5/3, or 1-2/3 feet per year.
4. Set up the ratios (0.5/12) = (x/180), since there are 180 minutes in three hours. Cross-multiplying gives you 12x = 90, x = 7.5 miles.
5. Set up the ratios (3/5)/1 = .6/1 = 7/x. Cross-multiplying, .6x = 7, x = 7/.6 = 11.66. You could make 11 batches, with a little flour left over.
6. Set up the ratios (342/12) = (x/1). Cross-multiplying, 12x = 340, so x = 28.5 miles/gallon.
7. Set up the ratios (5/8) = 40/x. So, cross-multiplying: 5x = 8 x 40 = 320, so x = 64 games.
8. The ratios are (.25/20) = (3.5/x). Cross-multiplying: .25x = 20 x 3.5 = 70, and x = 70/.25 = 280 miles.
9. Set up the ratios (300/12) = (400/x). then 300x = 400(12) = 4800, so x = 4800/300 = 16 hours.
10. The question basically asks whether two ratios are equal, or whether one is greater than the other. Since d = rt, t = d/r. If the two arrive at the same time, the ratios are equal: t = 10 miles/15 mph = 2 miles/3 mph. Indeed they are equal, so they arrive at the same time.
11. 3/(3+1) = x/800. 4x = 2400, so x = 600.
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