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?
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 $10.99. 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 $215.00. 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?
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.
13. Shopping at Savers Mart, Lisa buys her children four shirts and three pairs of pants for $85.50. She returns the next day and buys three shirts and five pairs of pants for $115.00. 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?
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.
22. The sum of two numbers is 40. Their difference is 16. Find the two numbers. 23. The total cost of two books is $32.90. 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?