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Solving Equations for Variables and Real-World Applications

This lesson explores solving equations for specific variables and applying formulas to real-world scenarios. It covers techniques such as dimensional analysis and the distributive property, offering examples like solving for fuel economy in vehicles and the geometry of cylinders. Learners will practice solving equations involving multiple variables, including isolating a single variable in terms of others. Each exercise provides step-by-step guidance on how to manipulate equations effectively, leading to practical problem-solving skills in mathematics.

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Solving Equations for Variables and Real-World Applications

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  1. Solve equations for given variables. • Use formulas to solve real-world problems. • dimensional analysis Lesson 8 MI/Vocab

  2. Solve an Equation for a Specific Variable Solve 5b + 12c = 9 for b. 5b + 12c = 9 Original equation 5b + 12c – 12c = 9 – 12c Subtract 12c from each side. 5b = 9 – 12c Simplify. Divide each side by 5. Simplify. Lesson 8 Ex1

  3. Solve an Equation for a Specific Variable Lesson 8 Ex1

  4. A. B. C. D.2x + 4 Solve 2x – 17y = 13 for y. • A • B • C • D Lesson 8 CYP1

  5. Solve an Equation for a Specific Variable Solve 7x – 2z = 4 – xy for x. 7x – 2z = 4 – xy Original equation 7x – 2z+ xy = 4 – xy + xy Add xy to each side. 7x – 2z + xy = 4 Simplify. 7x – 2z + xy+2z = 4 + 2z Add 2z to each side. 7x + xy = 4 + 2z Simplify. x(7 + y) = 4 + 2z Use the Distributive Property. Divide each side by 7 + y. Lesson 8 Ex2

  6. Solve an Equation for a Specific Variable Lesson 8 Ex2

  7. A. B. C. D. Solve 12a + 3c = 2ab + 6 for a. • A • B • C • D Lesson 8 CYP2

  8. A. FUEL ECONOMYA car’s fuel economy E (milesper gallon) is given by the formula , where mis the number of miles driven and g is the number of gallons of fuel used. Solve the formula for m. Formula for fuel economy Multiply each side by g. Answer:Eg = m Simplify. Lesson 8 Ex3

  9. B.FUEL ECONOMY If Claudia’s car has an average fuel consumption of 30 miles per gallon and she used 9.5 gallons, how far did she drive? Eg = m Formula for how many miles driven 30(9.5) = mE = 30 mpg and g = 9.5 gallons 285 = m Multiply. Answer: She drove 285 miles. Lesson 8 Ex3

  10. A. FUEL ECONOMYA car’s fuel economy E (milesper gallon) is given by the formula , where mis the number of miles driven and g is the number of gallons of fuel used. Solve the formula for g. A.g = mE B. m = gE C.D. • A • B • C • D Lesson 8 CYP3

  11. B.If Claudia drove 1477 miles and her pickup has an average fuel consumption of 19 miles per gallon, how many gallons of fuel did she use? • A • B • C • D A. 19 gallons B. 1477 gallons C. 77.74 gallons D. 80 gallons Lesson 8 CYP3

  12. A. GEOMETRYThe formula for the volume of a cylinder is V = πr2h, where r is the radius of the cylinder and h is the height. Solve the formula for h. Formula for volume of a cylinder Divide each side by πr2. Lesson 8 Ex4

  13. B. GEOMETRYWhat is the height of a cylindrical swimming pool that has a radius of 12 feet and a volume of 1810 cubic feet? Formula for h V = 1810 and r = 12 Use a calculator. Answer: The height of the cylindrical swimming pool is about 4 feet. Lesson 8 Ex4

  14. A. B. C. D.V = πr2v A. GEOMETRY The formula for the volume of a cylinder is V = πr2h, where r is the radius of the cylinder and h is the height. Solve the formula for r. • A • B • C • D Lesson 8 CYP4

  15. B. What is the radius of a cylindrical swimming pool if the volume is 2010 cubic feet and the height is 6 feet? • A • B • C • D A. 6 feet B. 2010 feet C. 20 feet D. 10 feet Lesson 8 CYP4

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