Word Problems: Number Theory and past/future Alg. 1H

Transcription

1 PS-A1 Word Problems: Number Theory and past/future Alg. 1H DO ON BINDER PAPER Define variables ("Let Statements"). Write a verbal model. Write an equation. Then solve your equation. Finally answer the problem asked. Remember: word problems need word answers. 1. The lengths of the sides of a triangle are consecutive odd integers. Find the length of the longest side if it is 20 units shorter than the perimeter. 2. The sum of two consecutive even integers is 126. Find the integers. 3. The sum of two consecutive integers is 243. What are the two integers? 4. There are three numbers. The first is twice as big as the second, and the second is twice as big as the third. The total of the numbers is 224. What is the smallest of the numbers? 5. There are 4 consecutive integers. The sum of the second and fourth equals the 3 rd increased by 17. Find them! 6. The smaller of 2 consecutive integers is four more than half the greater. Find them! 7. Jack is 8 years older than Hanna. Seven years ago, he was twice as old as Hanna. How old is each now? 8. Leo has $8 more than Karen and Karen has $15 more than Rex. If they $59 together, how much do each of them have? 9. One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now? 10. Five years ago, John s age was half of the age he will be in 8 years. How old is he now?

2 PS A2 Word Problems: Coin/Value problems Alg 1H 1. I have six more quarters than nickels. If the coins are worth $5.70, how many nickels are there? 2. Erica has ten more nickels than Vena has dimes. If Vena gave Erica eight of her dimes, then Vena would have the same amount of money as Erica. How much money do they have together? (Assume Erica initially has only nickels and Vena has only dimes.) 3. Warren has twice as many quarters as dimes and 3 more dimes than nickels. If he has $7 altogether, how many of each coin does he have? 4. Tickets for a play cost $6 for adults and $3 for students. There were twice as many children as adults and $4200 worth of tickets were sold. How many adult tickets were sold? 5. Tina s change of $13.50 consists of quarters and dimes. She received twice as many dimes as quarters. How many of each were there? 6. You have $440 in twenty, ten and five dollar bills. The numbers in that order are consecutive integers. How many of each bill do you have? 7. Jake has stamps that are worth $.25 and $.49. He has 3 times as many of the more expensive stamps than the less expensive. If he has $30.96 worth, how many of each type does he have? 8. A family bought 8 more $65 seats than $100 seats for an upcoming Dodger game. If they spent $2500 how many of each seat did they buy?

3 PS A-3 Word Problems: Rectangle/ Average Alg 1H 1. A rectangle is 8 ft x 9 ft. Its area is three times the area of another rectangle that is 12 ft. long. Find the width of the second rectangle. 2. The length of a rectangle is five less than twice the width. If the perimeter is 26 cm find the dimensions of the rectangle. 3. Suppose Kirk has taken three tests and made 88, 90, and 84. Kirk s teacher tells the class that each test counts the same amount. Kirk wants to know what he needs to make on the fourth test to have an overall average of 90 so he can make an A in the class. 4. Carla has four test scores of 84, 90, 86, and 93. There is one more test during the trimester. She wants to make an A in the class, which means she needs her average to be a 92. All five tests count the same (20% each) in determining the class grade. Is it possible for Carla to get an A in the class? 5. On the first of three tests, Sandra scored 74 points. On the third test, her score was 3 points more than on the second. Her average on the three tests was 85. What were her scores on the second and third tests? 6. The length of a rectangle is three times as long as its width. The perimeter is 56 cm more than the width. Find the rectangle s dimensions. 7. A rectangle is half as wide as it is long. If both the length and width are decreased by two cm. the perimeter would then be 64 cm. Find the dimensions of both rectangles. 8. The length of a green rug is 12 feet longer than its width. A gold rug is 2 feet wider and 3 feet shorter than the green rug and has a perimeter of 54 ft. find the dimensions of both rugs (Hint: use 2l + 2w =P for the gold rug 1 st ) 9. A wire that is 76 inches long is bent to form a rectangle. If the length of this rectangle is 7 inches less than twice its width, then what is the area of the rectangle?

4 PS-A4 Word Problems: Distance= Rate x Time Alg 1H 1. One car going 50 mph leaves three hours before a second car going 65 mph leaves. How many hours did it take for the second car to overtake the first? 2. Two cars, traveling toward each other at 50 and 60 mph, respectively, leave from points 880 miles apart. How long is it before they meet? 3. Jan and Susan are 400 miles apart. They decide to each travel 50 mph until they meet. Susan leaves at 9 AM, but Jan doesn't leave until 11 AM (two hours later). How many hours will Susan have to drive until she meets up with Jan? 4. A car started from Phoenix toward Los Angeles at the rate of 50 miles/hour. A second car left from the same place 1 hour later and drove along the same route at 65 miles/hour. How long did it take the second car to overtake the first? 5. The Lopez family drove from their house to Denton at 85 km/h. When they returned, the traffic was heavier and they drove at 68 km/h. The return trip took them 1 h longer. How long did it take them to drive home? 6. Todd can run at 9 m/s and Bruce can run at 8.5 m/s. On a race track Bruce is given a 15 m head start and the race ends in a tie. How long is the track? 7. A bus must travel at 45 miles per hour to make its 6 hour trip on time. During the first hour, the bus had to slow to 25 mi/h because of snow. What should its average speed be for the rest of the trip to be on time? 8. A car and a truck headed in the same direction left a parking lot at the same time. The car was 10 mi/h faster than the truck. Four hours later, the car arrived at its destination. The truck reached the same place an hour later. Find the speed of both vehicles. And how many miles did each vehicle drive?

5 PS-A5 Word Problems Ch 2: Mixed Practice Alg 1H 1. A coin bank contains dimes and quarters. The total amount of money is $ There are one and a half times more quarters than dimes. How many of each coin are there? 2. Eight years from now, the sum of Mike and Pele s ages will be 47. If Pele is now 4 years less than 4 times Mike s age, find their ages now. 3. Lola s scores in three bowling games were 160, 185, and 173. She needs an average score of at least 175 to win the championship. What is the minimum score Lola needs in the fourth game in order to win the championship? 4. I have 4 more quarters than dimes. If the coins are worth $3.80, how many of each coin do I have? 5. The lengths of the sides of a triangle are consecutive odd integers. If the perimeter is 1 less than four times the shortest side, find the length of each side. 6. Jo has nickels, dimes, and quarters worth $ She has 4 more quarters than nickels and twice as many nickels as dimes. How many dimes does Jo have? 7. Sara Jessup earns $6.00 an hour more than her assistant. During an 8-hour day they earn $240. How much does each earn per hour? 8. Allyson has taken four tests and made 82, 77, 75, and 84. She has to take a final exam and her teacher has told her that the final exam will count as two test grades. What does Allyson need to make on the final to get an 80%? 9. Hal makes $8 an hour working on Friday and $10 an hour working on Saturdays. Last week he made $112 working 4 more hours on Saturday than Friday. How many hours did he work on Saturday? 10. Ryan left the science museum and drove south for 3 hours. Gabriella left 2 hours later driving 42 km/h faster in an effort to catch up to him. After two hours more Gabriella finally caught up. Find Ryan's average speed.

6 PS-A6 Word Problems Mixed Practice Alg 1H 1. Two planes leave El Paso at 6:00 a.m., one flying east at a speed 20 km/h greater than the one traveling west. At 8:00 a.m. the planes are 1960 km apart. Find their speeds. 2. Two truck drivers started at the same time from towns 396 km apart and drove toward each other. One driver drove twice as fast as the other driver. If they met in 3 hours, find the speed of the slower driver. 3. A rectangle is 6 cm longer than it is wide. If the length is increased by 4 cm and the width is increased by 3 cm, the perimeter will be 58 cm. Find the dimensions of the original rectangle. 4. A car and a truck heading for Joliet on the same route left a restaurant parking lot at the same time. Their speeds differed by 10 mi/h. Four hours later the car arrived in Joliet. The truck reached Joliet one hour after the car. Find the speed of the car. 5. Layla is three times as old as Diana. In ten years, Layla will be twice as old as Diana. Find their present ages. 6. A father is three times the age of his son. In six years, the father will be 2.5 times the age of his son. How old are the father and son now? 7. Five years from now, Ernie will be twice Pete s age. If Ernie is now 2½ times as old as Pete find their ages. 8. The length of a rectangle is three times as long as its width. The perimeter is 45 cm more than the length. Find the rectangle s dimensions. 9. Two planes leave Kansas City at the same time, one traveling east and the other traveling west. The speed of the eastbound plane is 50 mph more than the speed of the westbound plane. After 2 hours, the planes are 2900 miles apart. What is the speed of the westbound plane? 10. The length of a rectangle is 8 cm more than the width. A second rectangle is 5 cm wider and 6 cm longer than the first rectangle. The second rectangle has a perimeter of 242 cm. Find the dimensions of each rectangle. (You may want to make a sketch first.)