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Write and Solve Equations

Write and Solve Equations. Learning Goal for Focus 2(HS.A-CED.A.1 , 2 & 3, HS.A-REI.A.1, HS.A-REI.B.3): The student will create equations from multiple representations and solve linear equations and inequalities in one variable explaining the logic in each step. Use Algebra to Solve Problems.

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Write and Solve Equations

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  1. Write and Solve Equations

  2. Learning Goal for Focus 2(HS.A-CED.A.1, 2 & 3, HS.A-REI.A.1, HS.A-REI.B.3): The student will create equations from multiple representations and solve linear equations and inequalities in one variable explaining the logic in each step.

  3. Use Algebra to Solve Problems • There are many ways to solve story problems: • Guess & check • Make a table • Look for a pattern • Draw a picture • Today you will write algebraic equations to solve problems. Images from http://schools.iclipart.com

  4. Getting a Speeding Ticket Greg lives in a state in which speeders are fined $15 for each mile per hour over the speed limit. Greg was given a ticket for $180 for speeding where the speed limit is 45 miles per hour. How fast was Greg driving? • Label what you know: • Speeding ticket = $180 • $15 per mile over limit • “x” how many miles over speed limit. • Write an equation. • 15x = 180 • Solve • x = 12 • Answer the question: • Greg was driving 57 miles per hour. Image from http://schools.iclipart.com

  5. The Gazelle and the Cheetah The gazelle can run 73 feet per second for several minutes. A cheetah can run faster (88 feet per second), but can only sustain its top speed for about 20 seconds. Gazelles seem to have an instinct for this difference because they will not run from a prowling cheetah until it enters their “safety zone.” This is the distance the cheetah would need to run to overtake the gazelle in 20 seconds if both are running at top speed. How close should the gazelle let the cheetah come before it runs? (Remember: d=rt) • Label what you know: • Gazelle’s distance = 73(20) • Cheetah’s distance = 88(20) • “x” buffer distance • Write an equation. • 73(20) + x = 88(20) • Solve • 1460 + X = 1760 • x = 300 • Answer the question: • The gazelle should not let the cheetah get closer than 300 feet. Images from http://schools.iclipart.com

  6. Money! Currently, you have $60 and your sister has $135. You decide to save $5 of your allowance each week, whereas your sister decides to spend her whole allowance plus $10 per week. How long will it be before you have as much as your sister? • Label what you know: • My starting amount= $60 • My savings each week= $5 • Her starting amount = $135 • Her spending each week = $10 • “w” number of weeks. • Write an equation. • 60 + 5w = 135 - 10w • Solve • 15w = 75 • w = 5 • Answer the question: • I will have as much as my sister in 5 weeks. Image from http://schools.iclipart.com

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