Name: ______Date: ______
Algebra Regents Review #2
Using Rates
1. Tom drove 290 miles from his college to home and used 23.2 gallons of gasoline. His sister, Ann, drove 225 miles from her college to home and used 15 gallons of gasoline. Whose vehicle had better gas mileage? Justify your answer.
3. The distance that Cynthia has driven is varying directly with the time she has been on the road. After two hours, she has driven a total of 124 miles. How far will she have driven after 5 hours?
Conversions
4. If the temperature in Buffalo is 23° Fahrenheit, what is the temperature in degrees Celsius?
[Use the formula C = (F – 32).]
6. The formula for changing Celsius (C) temperature to Fahrenheit (F) temperature is F = C + 32. Calculate, to the nearest degree, the Fahrenheit temperature when the Celsius temperature is -8.
Direct Variation
8. Nicole’s aerobic class exercises to fast-paced music. If the rate of the music is 120 beats per minute, how many beats would there be in class that is 0.75 hour long?
2. Lucy is driving on Interstate 84 at a constant speed. The distance that she drives varies directly with the amount of time she has been driving. Lucy drives 279 miles in the span of 4.5 hours.
(a) How far had Lucy driven after only 2 hours?
(b) How long did it take for Lucy to drive 217 miles?
(c) What is the speed that Lucy is driving?
5. On a certain day in Toronto, Canada, the temperature was 15° Celsius ©. Using the formula F = C + 32, Peter converts this temperature to degrees Fahrenheit (F). Which temperature represents 15° C in degrees Fahrenheit?
7. If the speed of sound is 344 meters per second, what is the approximate speed of sound, in meters per hour?
9. A cake recipe calls for 1.5 cups of milk and 3 cups of flour. Seth made a mistake and used 5 cups of flour. How many cups of milk should he use to keep the proportions correct?
10. If a machine that prints designs on R-shirts prints 500 shirts in 3 hours, how many hours will it take to print designs on 1,800 shirts?
12. Julio’s wages vary directly as the number of hours that he works. If his wages for 5 hours are $27.75, how much will he earn for 30 hours?
Speed
13. What is the speed, in meters per second, of a paper airplane that flies 24 meters in 6 seconds?
15. A rocket car on the Bonneville Salt Flats is traveling at a rate of 640 miles per hour. How much time would it take for the car to travel 384 miles at this rate?
(a) 36 minutes(c) 256 minutes
(b) 245 minutes(d) 1.7 hours
11. The table below represents the number of hours a student worked and the amount of money the student earned. Write an equation that represents the number
of dollars, d, earned in terms of the number of hours, h, worked. Using this equation, determine the number of dollars the student would earn for working 40 hours.
14. In a game of ice hockey, the hockey puck took 0.8 seconds to travel 89 feet to the goal line. Determine the average speed of the puck in feet per second.
16. Hannah took a trip to visit her cousin. She drove 120 miles to reach her cousin’s house and the same distance back home. It took her 1.2 hours to get halfway to her cousin’s house.
(a) What was her average speed, in miles per hour, for the first 1.2 hours of the trip?
(b) Hannah’s average speed for the remainder of the trip to her cousin’s house was 40 miles per hour. How long, in hours, did it take her to drive the remaining distance.?
(c) Traveling home along the same route, Hannah drove at an average rate of 55 miles per hour. After 2 hours her car broke down. How many miles was she from home?
17. The chart below compares two runners.
Based on the information in this chart, state which runner has the faster rate. Justify your answer.
Percents
19. A 14-gram serving of mayonnaise contains 11 grams of fat. What percent of the mayonnaise, the nearest tenth of a percent, is fat?
21. Linda paid $48 for a jacket that was on sale for 25% of the original price. What was the original price of the jacket?
23. A recent survey shows that the average man will spend 141,288 hours sleeping, 85,725 hours working, 81,681 hours watching television, 9,945 hours commuting, 1,662 hours kissing, and 363,447 hours on other tasks during his lifetime. What percent of his life, to the nearest tenth of a percent, does he spend sleeping?
25.The monthly budget for the front of the house is $8,000. You spent 6% of the budget on fresh flowers. How much did you spend on fresh flowers?
26.The world population was 4.2 billion people in 1982. The population in 1999 reached 6 billion. Find the percent of change from 1982 to 1999.
28. In 1998, Redview Elementary School had 418 students enrolled and in 1999, there were 354 students enrolled. What was the percent of change?
18. It takes Tammy 45 minutes to ride her bike 5 miles. At this rate, how long will it take her to ride 8 miles?
20. The Edison Lightbulb Company test 5% of their daily production of lightbulbs. If 500 bulbs were tested on Tuesday, what was the total number of bulbs produced that day?
22. Rashawn bought a CD that cost $18.99 and paid $20.51 including sales tax. What was the rate of the sales tax?
24. The Hudson Record Store is having a going-out-of- business sale. CDs normally sell for $18.00. During the first week of the sale, all CDs will sell for $15.00
(a) Written as a fraction, what is the rate of discount?
(b) What is this rate expressed as a percent? Round your answer to the nearest hundredth of a percent.
(c) During the second week of the sale, the same CDs will be on sale for 25% off the original price. What is the price of a CD during the second week of the sale?
27. In Cleveland, Ohio, the high temperature on one day was 43°F and the next day was 71°. Find the percent of change.
29. In 1955, there were 30 companies that manufactured marshmallows. Today, there are only about 6. Determine the percent change.