Systems of Equations-Application Problems. For the following, define your variables, write a system of equations, then solve.

Transcription

1 Systems of Equations-Application Problems Name For the following, define your variables, write a system of equations, then solve. 1. A length of ribbon 52 cm long is cut into two pieces. The first piece is 7 cm longer than twice the length of the second. How long is each piece? 2. A light plane flew from its home base to an airport 255 miles away. With a head wind, the trip took 1.7 hours. The return trip with a tail wind took 1.5 hours. Find the average airspeed of the plane and the average windspeed. 3. A quantity of 13% acid solution is being diluted with some 3% acid solution. The final solution must be 8% acid and contain 90 ml. How much of each solution is needed to accomplish this? 4. A quantity of 22% acid solution is being diluted with some 8% acid solution. The final solution must be 12% acid and contain 101 ml. How much of each solution is needed?

2 5. An orchestra consists of string instruments and wind instruments in a ratio of 9 to 4. There are 91string and wind instruments in the orchestra. How many of each instrument is in the orchestra? 6. Grandma s bakery sells single-crust apple pies for $6.99 and double-crust cherry pies for $ The total number of pies sold on a busy Friday was 36. If the amount collected that day was $331.64, how many of each type were sold? 7. Joe sold 56 tickets to the school play and collected $ Adult tickets cost $4.50 each and student tickets cost $3.50 each. How many of each kind did he sell? 8. John has dimes and quarters worth $4.50. He has 4 more quarters than dimes. How many of each type does he have?

3 9. Kay spends 250 min/week exercising. Her ratio of time spend on aerobics to time spent on weight training is 3 to 2. How many minutes per week does she spend on aerobics and weight training? 10. Mary ordered lunch for herself and several co-workers on Monday and Tuesday. On Monday she paid $7 for five sandwiches and four sodas. On Tuesday, she paid $6 for four of each. Find the price of a sandwich and the price of a soda. 11. Milk that is 2% butterfat is mixed with milk that is 4% butterfat to obtain 10 gallons of milk that is 3.25% butterfat. How many gallons of 2% and 4% are needed? 12. On a canoe trip, Rita paddled upstream at an average speed of 2 mi/h relative to the riverbank. On the return trip downstream, her average speed was 3 mi/h. Find Rita s paddling speed in still water and the speed of the river s current.

4 13. Shopping at Savers Mart, Lisa buys her children four shirts and three pairs of pants for $ She returns the next day and buys three shirts and five pairs of pants for $ What is the price of each shirt and each pair of pants? 14. Suppose you are canoeing along a river with a steady current. Your average speed upstream is 2.5 mi/h. On the return trip you paddle with the current, and your average speed is 4 mi/h. Find the average speed of the current and your average speed paddling. 15. Suppose you are starting an office-cleaning service. You have spent $315 on equipment. To clean an office, you use $4 worth of supplies. You charge $25 per office. How many offices must you clean to break even? 16. Suppose you bought supplies for a party. Three rolls of streamers and 15 party hats cost $30. Later, you bought 2 rolls of streamers and 4 party hats for $11. How much did each roll of streamers and each party hat cost?

5 17. Suppose you spend $500 on an oven to bake bread. Each loaf of bread costs you $.20 to bake. You sell the loaves for $1.00 each. How many loaves of bread must you sell to break even? 18. The math club and the science club had fundraisers to buy supplies for a hospice. The math club spent $135 buying six cases of juice and one case of bottled water. The science club spent $110 buying four cases of juice and two cases of bottled water. How much did a case of bottles water and a case of juice cost? 19. The measure of one complementary angle is 6 less than twice the other. Find the measure of each angle. 20. The ratio of boys to girls at an after school dance is 2 to 5. If 350 tickets were sold, how many girls were at the dance? 21. The ratio of one supplementary angle to another is 7:2. Find the measure of the obtuse angle.

6 22. The sum of two numbers is 40. Their difference is 16. Find the two numbers. 23. The total cost of two books is $ The hardcover book is $3 more than the paperback. Find the cost of each book. 24. Three pairs of sneakers and 2 pairs of socks cost $78. Two pairs of sneakers and 4 pairs of socks cost $60. Find the cost of one pair of sneakers and one pair of socks. 25. While on vacation, Kevin went for a swim in a nearby lake. Swimming against the current, it took him 8 minutes to swim 200 meters. Swimming back to short with the current took half as long. Find Kevin s average swimming speed and the speed of the lake s current. 26. You have a total of 25 coins, all nickels and quarters. The total value is $3.85. How many quarters and how many nickels do you have?