1. Math Pacing Solving Equations and Formulas

3. Some equations such as the one on the previous slide contain more than one variable. At times, you will need to solve these equations for one of the variables.

4. Solve for b. Example 8-1a Original equation Simplify. Subtract 12c from each side. Divide each side by 5. Solve and Equation for a Specific Variable

5. Example 8-1b or Simplify. Answer: The value of b is. Solve and Equation for a Specific Variable

6. Solve for y. Example 8-1c Answer: The value of y is. Solve and Equation for a Specific Variable Do this one in your notes, please! Add 17y to both sides Subtract 13 from both sides Divide both sides by 17

7. Solving Equations and Formulas Many real-world problems require the use of formulas. Sometimes solving a formula for a specific variable will help you solve the problem.

8. Fuel Economy A car’s fuel economy E (miles per gallon) is given by the formula, where m is the number of miles driven and g is the number of gallons of fuel used. Solve the formula for m. Example 8-3a Use a Formula to Solve a Problem

9. Example 8-3b Formula for fuel economy. Simplify.Answer: Multiply each side by g. Use a Formula to Solve a Problem

10. Example 8-3c 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? Formula for how many miles driven E = 30 mpg and g = 9.5 gallons Multiply. Answer: She drove 285 miles. Use a Formula to Solve a Problem

11. Example 8-3d Fuel Economy A car’s fuel economy E (miles per gallon) is given by the formula, where m is the number of miles driven and g is the number of gallons of fuel used. Solve the formula for g. Answer: Use a Formula to Solve a Problem Do this one in your notes, please!

12. Example 8-3e 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? Answer: She used around 77.74 gallons. Use a Formula to Solve a Problem Fuel Economy A car’s fuel economy E (miles per gallon) is given by the formula, where m is the number of miles driven and g is the number of gallons of fuel used.

13. Geometry The formula for the volume of a cylinder is, where r is the radius of the cylinder and h is the height. Solve the formula for h. Example 8-4a Original formula Answer: Divide each side by. Use Dimensional Analysis

14. Example 8-4b Geometry What is the height of a cylindrical swimming pool that has a radius of 12 feet and a volume of 1810 cubic feet? Answer:The height of the cylindrical swimming pool is about 4 feet. Formula for h Use Dimensional Analysis V = 1810 and r = 12 Use a calculator.

15. Example 8-4c Answer: Geometry The formula for the volume of a cylinder is, where r is the radius of the cylinder and h is the height. Solve the formula for r. Use Dimensional Analysis Do this one in your notes, please!

16. Example 8-4d What is the radius of a cylindrical swimming pool if the volume is 2010 cubic feet and a height of 6 feet? Answer: The radius is about 10.3 feet. Use Dimensional Analysis Do this one in your notes, please! 2010 = 3.14 r 2 6106.6 ≈ r 2