Algebra 2: Linear Equations and Inequalities in One Variable Topic B2: Formulas | VERSION B Name: ___________________________________________ 1. Find 𝑦 when 𝑥 is 3: 3𝑥 + 4𝑦 = 7. 2. Find 𝑥 when 𝑦 is 4: 𝑦 = 𝑥 + 5. 3. If 𝑥 + 𝑦 = 5 and 𝑦 = , find 𝑥. 5 2 6. Use the formula 𝑑 = 𝑟 − 𝑐 𝑡 to find 𝑐 if 𝑑 = 15, 𝑟 = 6, and 𝑡 = 3. 7. If 𝑉 = , find 𝐾 if 𝑉 = 39 and 𝑃 = 46. 8. Solve the following for value of l : 𝐴 = 𝑙𝑤. 𝐾 𝑃 Solve for 𝑦. 4. Find 𝑅 if 𝑝 = 2.5 and 𝑅 = 1300 − 200𝑝 𝑝. 9. −2𝑥 − 𝑦 = 3 10. 4𝑥 + 3𝑦 = −24 5. Find 𝑃 if 𝑃 = −0.1𝑥 ! + 33𝑥 + 2,700 and if 𝑎. 𝑥 = 180, 𝑃 = 𝑏. 𝑥 = 150, 𝑃 = 11. 4𝑦 − 6𝑥 = 5 www.varsitylearning.com 1 Algebra 2: Linear Equations and Inequalities in One Variable Topic B2: Formulas | VERSION B Name: ___________________________________________ 12. 𝑎𝑦 − 2 = 𝑏𝑦 + 1 17. Find the value of −3𝑥 + 3 when 𝑥 is 1. 13. 𝑥 = 5𝑦 − 1 18. If you can measure the area that the tires on your car contact the ground and know the air pressure in the tires, then you can estimate the weight of your car with the following formula: 𝑊 = 15. 𝑏 . 𝑦+4 = 5 𝑥+6 𝑐 . 𝑦−1 = 0 𝑥−3 ! ! where 𝑊 is the vehicle's weight in tons, 𝐴 is the average tire contact area with a hard surface in square inches, 𝑃 is the air pressure in the tires in pounds per square inch (psi, or lb/in^2), and 𝑁 is the number of tires. What is the approximate weight of a car if the average tire contact area is a rectangle 5 inches by 4 inches and if the air pressure in the tires is 30 psi? The car weighs about tons. 𝑦−1 = 2 𝑥+0 14. 𝑎 . + ! ! = 1 16. −3𝑦 + 3 = 9 𝐴𝑃𝑁 2,000 19. It takes a boat 4 hours to travel 28 miles upstream against a current. If the speed of the boat in still water is 10 miles per hour, what is the speed of the current? The speed of the current is miles per hour. 20. An airplane takes 6 hours to travel 1188 miles while flying against the wind. If the speed of the airplane on a windless day is 237 miles per hour, what is the speed of the wind? The wind is miles per hour. www.varsitylearning.com 2 Algebra 2: Linear Equations and Inequalities in One Variable Topic B2: Formulas | VERSION B Name: ___________________________________________ 1 2 1. Find 𝑦 when 𝑥 is 3: 3𝑥 + 4𝑦 = 7. 𝑦 = − 6. Use the formula 𝑑 = 𝑟 − 𝑐 𝑡 to find 𝑐 if 𝑑 = 15, 𝑟 = 6, and 𝑡 = 3. 𝑐 = 1 2. Find 𝑥 when 𝑦 is 4: 𝑦 = 𝑥 + 5. 𝑥 = −1 7. If 𝑉 = , find 𝐾 if 𝑉 = 39 and 𝑃 = 46. 𝐾 = 1,794 8. Solve the following for value of l : 𝐴 = 𝑙𝑤. 𝑙 = 3. 5 5 If 𝑥 + 𝑦 = 5 and 𝑦 = , find 𝑥. 𝑥 = 2 2 𝐾 𝑃 𝐴 𝑤 Solve for 𝑦. 4. Find 𝑅 if 𝑝 = 2.5 and 𝑅 = 1300 − 200𝑝 𝑝. 𝑅 = 2,000 9. −2𝑥 − 𝑦 = 3 𝑦 = −2x − 3 10. 4𝑥 + 3𝑦 = −24 𝑦 = − 5. 4𝑥 − 8 3 Find 𝑃 if 𝑃 = −0.1𝑥 ! + 33𝑥 + 2,700 and if 𝑎. 𝑥 = 180, 𝑃 = 5,400 𝑏. 𝑥 = 150, 𝑃 = 5,400 11. 4𝑦 − 6𝑥 = 5 𝑦 = 3𝑥 5 + 2 4 www.varsitylearning.com 3 Algebra 2: Linear Equations and Inequalities in One Variable Name: ___________________________________________ Topic B2: Formulas | VERSION B 12. 𝑎𝑦 − 2 = 𝑏𝑦 + 1 𝑦 = 3 𝑎−𝑏 𝑥+1 13. 𝑥 = 5𝑦 − 1 𝑦 = 5 17. Find the value of −3𝑥 + 3 when 𝑥 is 1. 0 18. If you can measure the area that the tires on your car contact the ground and know the air pressure in the tires, then you can estimate the weight of your car with the following formula: 𝑊 = 14. 𝑎 . 𝑦−1 = 2 𝑦 = 2𝑥 + 1 𝑥+0 𝑏 . 𝑦+4 = 5 𝑦 = 5𝑥 + 26 𝑥+6 𝑐 . 𝑦−1 = 0 𝑦 = 1 𝑥−3 15. ! ! + ! ! = 1 𝑦 = 9 − 𝐴𝑃𝑁 2,000 where 𝑊 is the vehicle's weight in tons, 𝐴 is the average tire contact area with a hard surface in square inches, 𝑃 is the air pressure in the tires in pounds per square inch (psi, or lb/in^2), and 𝑁 is the number of tires. What is the approximate weight of a car if the average tire contact area is a rectangle 5 inches by 4 inches and if the air pressure in the tires is 30 psi? The car weighs about 1.2 tons. 19. It takes a boat 4 hours to travel 28 miles upstream against a current. If the speed of the boat in still water is 10 miles per hour, what is the speed of the current? The speed of the current is 3 miles per hour. 3𝑥 2 16. −3𝑦 + 3 = 9 𝑦 = −2 20. An airplane takes 6 hours to travel 1188 miles while flying against the wind. If the speed of the airplane on a windless day is 237 miles per hour, what is the speed of the wind? The wind is 39 miles per hour. www.varsitylearning.com 4