Algebra 1 – Chapter 7 Word Problem Packet Name: ______________________________________ Chapter 7 Word Problem Packet 1) Is it possible to have $24 in dimes and nickels and have four times as many nickels as dimes? Equation: 2) A bag of coins contains nickels and quarters. It contains eight more quarters than nickels. The total value of the money is $5.00. How many of each coin does the bag contain? Equation: 2
3) The most popular items sold at the Taco Hut are tacos and sodas. Jim can purchase 5 tacos and 2 drinks for $5.50. Susan can purchase 2 tacos and 1 drink for $2.35. What is the price of each item? Equation: 4) A grocer blends Ceylon tea selling at $1.50 per pound with orange pekoe tea selling at $2.50 per pound to make a blend selling at $2.00 per pound. How many pounds of each kind should be used to make a mixture of 100 pounds? Equation: 3
5) Becky starts from a certain point, traveling four mph. Five hours later, Ella starts from the same point and travels in the same direction at eight mph. In how many hours will Ella overtake Becky? Equation: 6) How many quarts of solvent containing 50 percent acetone must be added to 20 quarts of solvent containing 4 percent acetone to produce a mixture containing 20 percent acetone? Equation: 4
7) One kind of candy sells for $2.00 a pound and another kind sells for $5.00 a pound. How many pounds of each kind should be used to form a mixture of 60 pounds that will sell for $3.50 a pound? Equation: 8) Tickets for a concert cost $8 for adults and $4 for students. A total of 920 tickets worth $5760 were sold. How many adult tickets were sold? Equation: 5
9) Jordan went to Office Max and bought 8 pencils and 7 erasers for $3.37. The next week he bought 5 pencils and 11 erasers for $3.10. What is the price of each item? Equation: 10) A metal alloy is 25 % copper. Another metal alloy is 50 % copper. How much of each alloy should be used to make 1000 grams of a metal alloy that is 45% copper? Equation: 11)The sum of two numbers is 27. Their difference is 5. Find the numbers. 6
12) Abigail and Lila travel from the same point in opposite directions. Abigail travels 20 mph faster than Lila. How fast did each travel if there were 250 miles apart at the end of four hours? Equation: 13) At 3 p.m., a train traveling at 60 mph started from Newberry to Columbia. At 4 p.m., a train traveling 40 mph started from Columbia travel toward Newberry. Newberry is 500 miles from Columbia. When will the engines of the two trains pass each other? Equation: 7
14) A boat travels 18 miles downstream in 2 hours. It requires 6 hours to travel back to its starting point upstream. What is the rate of the boat in still water and what is the rate of the current? Equation: 15) Toni has a collection of dimes and quarters having a face value of $25.30. She has 27 more quarters than she does dimes. How many of each coin does Toni have? Equation: 8
Algebra 1 – Word Problems Name: _______________________________________ 1. The bank has a large display of an equal number of pennies and nickels. The value of the coins in the display is $24. How many of each coin is in the display? 2. The sum of two numbers is 135. The difference between them is 9. Find the numbers. 3. A store owner has two different blends of coffee. Coffee A sells for $10.50 per lb and Coffee B sells for $5.75 per lb. The owner wants to create a 25‐lb mix of the two that will sell for $8.22 per lb. How many pounds of each blend should he use? 4. A sporting goods store sells right‐handed and left‐handed baseball gloves. In one month, 12 gloves were sold for a total of $561. Right‐handed gloves cost $45 and left‐handed gloves cost $52. How many of each type of glove did they sell? 5. Your family goes to a Southern‐style restaurant for dinner. There are 6 people in your family. Some people order the chicken dinner for $14 and some ordered the steak dinner for $17. If the total bill was $99 (without tax), how many people ordered each dinner? 6. You are making a saline solution in science class. One hundred milliliters of 50% saline solution is obtained by mixing a 40% saline solution with a 60% saline solution. How much of each must you use? 7. Ben can purchase office supplies for his store from several companies. From Pirates Wholesale, Ben can purchase 100 pens and 200 pencils for $125. Bulldog Supply will sell him 500 pens and 200 pencils for $425. Assuming that the pens and pencils are the same price at both companies, how much will Ben pay for each pen and pencil? 8. Darren and Maria took several buses and subways to meet for lunch in New York City. Darren took two buses and two subways. It cost him $2.60 one way. Maria took one bus and three subways for a one‐way cost of $2.40. What are the bus and subway fares? 9. Burger Buddy sells Big Burgers and sodas at the high school soccer games. Jana pays $13.40 to buy four Big Burgers and four sodas for herself and three friends. Lars pays $9.20 to buy three Big Burgers and two sodas for himself and his brother. What is the price of one Big Burger and one soda? 10. The sum of 2 numbers is 128. Their difference is 114. Find the numbers. 11. Todd purchased 2 CD’s and 3 DVD’s for $75. Paula went to the same music store and purchased 1 CD and 5 DVD’s for $76. How much was each CD and DVD? 12. You are making 10 tons of concrete that is 40 % cement by mixing a 20 % cement mixture with a 70% cement mixture. How much of each must you use? 13. One number is 8 more than the other. Their sum is 32. Find the two numbers. 9
14. A grocer sells coffee from Brazil for $3.00 per pound and coffee from Colombia for $4.00 per pound. How many pounds of each should be used in order to sell the blend of 100 pounds for $3.50 per pound? 15. Jan buys 4 candy bars and 2 sodas for $4.80. Tom buys 3 candy bars and 4 sodas for $6.10. How much is a candy bar and how much is a soda? 16. A riverboat on the Mississippi River travels 48 miles upstream in 4 hours. The return trip takes the riverboat only 3 hours. The speed of the current remains the same during the travel upstream and downstream. Find the rate of the current. 17. An airplane travels 1560 miles in 3 hours flying with the wind. The speed of the wind remains the same during the travel with and against the wind. The return trip takes 4 hours. Find the rate of the plane in still air. 18. During a kayaking trip, a kayaker travels 12 miles upstream (against the current) in 3 hours, and 12 miles downstream (with the current) in 2 hours. The speed of the current remained constant during the trip. Find the average speed of the kayak in still water and the speed of the current. 19. Sara leaves home at 7 A.M. traveling at a rate of 45 mi/hr. Her son discovers that she has forgotten her briefcase and starts out to catch up with her. Her son leaves at 7:30 A.M. at a rate of 55 mi/h. At what time will he overtake his mother? 20. While driving to Port Washington, Mrs. Sumner travels at an average speed of 40 mph. On the return trip, she travels at an average speed of 56 mph and saves two hours of travel time. How far does Mrs. Sumner live from Port Washington? 21. Carl and Fred started driving from the same point, Carl traveling due east and Fred traveling due west. The rate at which Carl drove was twice that of Fred. After four hours, they were 600 miles apart. Find the rate of each. 22. A riverboat travels 28 miles downstream in 5 hours. It travels 28 upstream in 7 hours. The speed of the current remains the same during the travel upstream and downstream. Find the average speed of the riverboat in still water and the speed of the current. 23. The air speed of a small plane was 200 mph. The plane could travel from Denver to Carlsbad in Four hours with the wind. It flew from Carlsbad to Denver in six hours against the wind. Find the wind speed. 10
Algebra 1 – Word Problems Packet Systems Review 1. Solve the linear system by graphing. 1
3
5
3. Use substitution to solve the linear system. 4
1
2
7
4. Use elimination to solve the linear system. 3
4
5
5
4
13
5. Solve using any method. 2
4
3
4
4
6
2. Solve the linear system by graphing. Name: ______________________________________ 2
3
11
6. Use substitution to solve the linear equation. 4
23
3
4
7. Solve using any method. 4
4
5
8. Solve using any method. 2
1
3
9
9. Solve using any method. 9
7
77
3
9
3
10. Use elimination to solve the linear system. 4
3
2
3
2
3
12
11. Solve using any method. 3
2
3
6
2
3
12. Solve using any method. 5
5
32
3
3
14
13