Write, Solve, and Graph Equations
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
Getting a Speeding Ticket 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. 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? Image from http://schools.iclipart.com
Getting a Speeding Ticket Greg lives in a state in which speeders are fined $15 for each mile per hour over the speed limit. Write an equation that will determine the cost “C” for any speeding ticket that is written. Graph your equation. Cost of a Speeding Ticket Label what you know: Speeding ticket = C $15 per mile over limit “x” how many miles over speed limit. Write an equation. 15x = C Make a Graph Start with a t-chart to know what values your graph will need to be. Plot your points and connect them. 210 195 180 165 C O S T $ 150 135 120 105 90 75 60 45 30 15 Miles over the Speed Limit
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
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. Write an equation that will calculate the total, T, you have after w amount of weeks. Write an equation that will calculate the total, T, your sister will have after w amount of weeks. Graph both equations on the same graph. Comparing our Money 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 your equation. 60 + 5w = T Write your sister’s equation. 135 - 10w = T Make a Graph Start with a t-chart to know what values your graph will need to be. Plot your points and connect them. 140 130 120 110 100 90 T O A L $ 80 70 60 50 40 30 20 10 Number of Weeks
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