Applications of Linear Systems Homework Days 3-5 (2)

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Jan 9, 2024

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Applications and Problem Solving 4. Numbers The sum of two numbers is 255. When the smaller is subtracted from the larger, the result is 39. Find the numbers. 5. Earning interest Isabel invested $8000, part at 9% per annum and the remainder at 4% per annum. After one year, the total interest from these investments was $420. How much did she invest at each rate? 6. Driving Kareem took 5 h to drive 470 km from Sudbury to Brantford. For part of the trip, he drove at 100 km/h. For the rest of the trip, he drove at 90 km/h. How far did he drive at each speed? 7. Patrol boat It took a patrol boat 5 h to travel 60 km up a river against the current, and 3 h for the return trip with the current. Find the speed of the boat in still water and the speed of the current. 8. Investments Hakim invested $15 000. He put part of it in a term deposit that paid 4% per annum, and the remainder in a treasury bill that paid 5% per annum. After one year, the total interest was $690. How much did Hakim invest at each rate? 8. Measurement Find the values of x and 9. e XN /QX—}/)‘ (3x + 2y)° B > > 77 587 10. Vinegar solutions White vinegar is a solution of acetic acid in water. There are two strengths of white vinegar—a 5% solution and a 10% solution. How many millilitres of each solution must be mixed to make 50 mL of a 9% vinegar solution? 11. Acid solutions What volume, in millilitres, of a 60% hydrochloric acid solution must be added to 100 mL of a 30% hydrochloric acid solution to make a 36% hydrochloric acid solution? 12. Measurement Use the diagram to find the values of x and y. . \124° B (2x + 3y) Yx -2y) 13. Flying speed A plane took 4 h to fly 2200 km from Saskatoon to Toronto with a tail wind. The return trip, with a head wind, took 5 h. Find the speed of the plane in still air and the wind speed. 14. Pool table The perimeter of a pool table is about 7.8 m. Four times the length equals nine times the width. What are the dimensions of the table, in metres? 15. Fitness Playing tennis burns energy at a rate of about 25 kJ/min. Cycling burns energy at about 35 kJ/min. Hans exercised by playing tennis and then cycling. He exercised for 50 min altogether and used a total of 1450 kJ of energy. For how long did he play tennis? 3 16. Measurement The rectangle has an area of 7 square units and a perimeter of 27z units. - What is the value of «? 17. Driving distance Erica drove from Sarnia at 80 km/h. Aisha left Sarnia one hour later and drove along the same road at 100 km/h. How far from Sarnia did Aisha overtake Erica? Answers Applications and Problem Solving 4. 147, 108 5. $2000 at 6%, $6000 at 4% 6. 200 km at 100 km/h, 270 km at 90 kim/h 7. 16 kin/h, 4 kin/h 8. S6000 at 4%, $9000 at 5% 9.a =34, y=10 10. 10 mL of the 5% solution, 40 mL of the 10% solution 11.25 mL 12, v =32,y =20 13.495 km/h, 55 kin/h 14. 2.7 m by 1.2 m 15.30 min 16. 2.5 17. 400 km
13. Resort costs A weekend at Bayview Lodge costs $360 and includes two nights’ accommodation and four meals. A week costs $1200 and includes seven nights’ accommodation and ten meals. If 7 represents the cost of one night, and 7 represents the cost of one meal, the relationship between the costs can be modelled by the following system of equations. 2n + 4m = 360 7n + 10m = 1200 Determine the cost of one night and the cost of one meal. 14. Car wash The Outdoors Club held a car wash to raise money. They washed cars for $5 each and vans for $7 each. They washed 45 vehicles and earned $243. How many of each type of vehicle did they wash? 15. Buying bonds Li bought a Canada Savings Bond paying 5.5% interest and a provincial government bond paying 6.5% interest. She invested a total of $15 000 and earned $925 in interest in the first year. How much did she pay for each bond? 16. Lawn fertilizer One lawn fertilizer is 24% nitrogen, and another is 12% nitrogen. How much of each fertilizer should be mixed to obtain 100 kg of fertilizer that is 21% nitrogen? 17. Tail wind A small plane took 3 h to fly 960 km from Ottawa to Halifax with a tail wind. On the return trip, flying into the wind, the plane took 4 h. Find the wind speed and the speed of the plane in stll air. 18. Car trip Maria drove from Owen Sound to Ottawa, a distance of 550 km. The trip took 7 h. Maria drove at 70 km/h for part of the trip, and at 85 km/h for the remainder of the trip. How far did she drive at 70 km/h? Answers 13. one night: $150, one meal: $15 14. 36 cars and 9 vans 15. $5000 Canada Savingy Bond, $10 000 Provincial Government Bond 16. 75 kg of 24% nitrogen, 25 kg of 12% nitrogen 17. 40 kain/h; 280 km/h 18. 210 km 7. Longest rivers The Mackenzie, the longest river in Canada, is 1056 km longer than the Yukon, the second longest river. The total length of the two rivers is 7426 km. Find the length of each river. 8. Granola One type of granola is 30% fruit, and another type is 15% fruit. What mass of each type of granola should be mixed to make 600 g of granola that is 21% fruit? 9. Investments Zach invested in a term deposit that paid 4% interest per annum and in a municipal bond that paid 6% interest per annum. If he invested a total of $13 000 and earned $700 interest in a year, how much did he invest at each rate? 10. Flying speeds A plane flew 3000 km from Calgary to Montréal with the wind in S h. The return flight into the wind took 6 h. Find the wind speed and the speed of the plane in still air. Answers 7. Mackenzie River: 4241 km. Yukon River: 3185 km 8. 240 g of 30% fruit, = of 15% fruit 9. term deposit: $4000, municipal fw= $9000 10. 50 km/h, 550 km/h -
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