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# 8 - using linear equations to solve word problems

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### 8 - using linear equations to solve word problems

1. 1. Using linear equations to solve wor d pr oblems Usually deal with changes over Usually deal with changes over time.PPT File Name: F:TeachingNorth East Carolina Prep SchoolLesson PlansMathAssigments8 -- Using Linear Equations to Solve Word ProblemsPPT URL: http://www.slideshare.net/Anthony_Maiorano/8-using-linear-equations-to-solve-word-problems or http://bag.sh/26kuNotes File Name: F:TeachingNorth East Carolina Prep SchoolLesson PlansMathAssigments8 – Using Linear Equations to Solve Word ProblemsNotes URL: http://www.scribd.com/doc/134269678/8-%E2%80%93-Using-Linear-Equations-to-Solve-Word-Problems
2. 2. Common Core Common Core Common Core 8.EE.B.6: Understand the  8.F.B.4: Use functions to model connections between relationships between proportional relationships, quantities. Construct a function to lines, and linear equations. Use model a linear relationship similar triangles to explain why the between two quantities. Determine slope m is the same between any the rate of change and initial two distinct points on a non- value of the function from a vertical line in the coordinate description of a relationship or plane; derive the equation y = mx from two (x, y) values, including for a line through the origin and reading these from a table or from the equation y = mx + b for a line a graph. Interpret the rate of intercepting the vertical axis at b. change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
3. 3. ¿Essential Question? How can you utilize a linear equation in two variables to model and solve real life problems?
4. 4. Vocabulary Linear Equation: algebraic equation in which each term is either a constant or the product of a constant and the first power of a single variable Functions: a mathematical relationship between two values. The second value determines the first. y = 2x Value: a numerical worth or amount Variable: a quantity that can change represented by a letter. x or y
5. 5. How do youUNRAAVEL?U nderline the questionN ow predict what you think you need to do to solve the problemR ead the word problemA re the important words circled? (especially clue words)A pply the step(s) you chose to solve the problemV erify your answer (is it reasonable; does it make sense?)E liminate wrong answersL et the answer stay or rework the problem Double check your work!
6. 6. Y intercept does notchangeSlope does change   Example: Kim wants to rent a car on the Big Island. Mr. Lee’s Rentals rents cars for \$99.00 for one week plus \$0.11 per mile over 100 miles. If Kim drives 400 miles, how much does she pay?
7. 7. y=mx +/-b. y = .11x+99  The weekly rental rate does not change. It is the y-intercept, and it’s \$99.00.  The amount of miles changes, so it is the slope. The slope is the rate of change: \$.11 per mile over 100 miles.  Let x = the number of miles she drives over 100 miles.
8. 8. Example #2: y=5x+10 Bobby charges \$10. per lawn he mows, and an additional \$5. per hour. What does not change? What is the y- intercept? \$10.00 per lawn What changes? What is the slope? The \$5. per hour depending on how many hours it takes to mow the lawn Let x = the number of hours it takes to mow a lawn.
9. 9. Create a My Way Make up a word problem where something is constant (does not change) and something does change. State the y-intercept State the slope State what the variable (the “x”) is
10. 10. Examples of WordProblems for My Way Cell Phone: \$50. monthly rate + .12 cents a minute over 300 minutes. Let x = # of minutes over 300. T-shirt company charges \$24. per order plus \$12.00 per shirt. Let x = the # of shirts ordered.Yoga classes: \$10 for sign-up plus \$5. per class
11. 11. STEPS IN SOLVING WORDPROBLEMS WITH LINEARALGEBRA  1. Define the variable that you want to find with a let statement. Let x = ….  2. Create an equation that expresses the information given in the problem’s scenario. Decide on the y- intercept and the slope (rate of change)  3. Solve your equation using algebraic methods.  4. Consider if your answer is reasonable.  5. Label your solution appropriately.  6. Check your answer with the conditions given in the problem.
12. 12. VideoKhan Academy Video on “Basic Linear “Equation Word Problem” detailsConstructing and solving a basic equationbased on a word problem. URL: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/basic-equation-practice/v/basic-linear-equation-word-problem
13. 13. Problem 1aTo move up to the maestro levelin his piano school, Ishaan needs tomaster at least 80 songs.Ishaan hasalready mastered 16 songs. If Ishaan can typically master 4 songs permonth, what is the minimum numberof months it will take him to move tothe maestro level?
14. 14. Problem 1bTo move up to the maestro To solve this, lets setlevel in his pianoschool, Ishaan needs to up an expression tomaster at least 80 songs. show how manyIshaan has alreadymastered 16 songs. If Ishaan songs Ishaan will havecan typically master 4 songs mastered after eachper month, what is the month.minimum number of months itwill take him to move to themaestro level?
15. 15. Problem 1cTo move up to the maestro Number of songslevel in his pianoschool, Ishaan needs to masteredmaster at least 80 songs.Ishaan has already =mastered 16 songs. If Ishaan Months at schoolcan typically master 4 songsper month, what is the ×minimum number of months itwill take him to move to the Songs mastered permaestro level? month + Songs already mastered
16. 16. Problem 1dTo move up to the maestro Since Ishaan needs tolevel in his pianoschool, Ishaan needs to have at least 80 songsmaster at least 80 songs. mastered to move toIshaan has alreadymastered 16 songs. If Ishaan maestro level, we cancan typically master 4 songs set up an inequality toper month, what is the find the number ofminimum number of months itwill take him to move to the months neededmaestro level?
17. 17. Problem 1eTo move up to the maestro  Number of songslevel in his pianoschool, Ishaan needs to mastered ≥80master at least 80 songs.Ishaan has already Number of songs masteredmastered 16 songs. If Ishaancan typically master 4 songs =per month, what is the Months at schoolminimum number of months it ×will take him to move to the Songs mastered per monthmaestro level? + Songs already mastered
18. 18. Problem 1fTo move up to the maestro We are solving for thelevel in his pianoschool, Ishaan needs to months spent atmaster at least 80 songs. school, so let theIshaan has alreadymastered 16 songs. If Ishaan number of months becan typically master 4 songs represented by theper month, what is the variable x.minimum number of months itwill take him to move to themaestro level? y = mx+b y = mx+b
19. 19. Problem 1gTo move up to the maestro y = mx+blevel in his pianoschool, Ishaan needs to y = mx+bmaster at least 80 songs.Ishaan has alreadymastered 16 songs. If Ishaan We can now plug in:can typically master 4 songsper month, what is the 80 = 4x +16minimum number of months itwill take him to move to themaestro level?
20. 20. Problem 1h Two step EquationTo move up to the maestro  We can now plug in:level in his pianoschool, Ishaan needs to 80 = 4x +16master at least 80 songs.Ishaan has alreadymastered 16 songs. If Ishaancan typically master 4 songsper month, what is the 80 = 4x +16minimum number of months itwill take him to move to the -16 = 4x -16maestro level? 64 = 4x
21. 21. Problem 1iTo move up to the maestrolevel in his pianoschool, Ishaan needs tomaster at least 80 songs.Ishaan has alreadymastered 16 songs. If Ishaancan typically master 4 songsper month, what is theminimum number of months itwill take him to move to themaestro level?
22. 22. Problem 1jTo move up to the maestrolevel in his pianoschool, Ishaan needs to Ishaan must work 16master at least 80 songs.Ishaan has already monthsmastered 16 songs. If Ishaancan typically master 4 songsper month, what is theminimum number of months itwill take him to move to themaestro level?
23. 23. Problem 2aFor every level Kevin completes in his favoritegame, he earns 800 points. Kev already has 450points in the game and wants to end up with atleast 3,390 points before he goes to bed. What isthe minimum number of complete levelsthat Kevin needs to complete to reach his goal?
24. 24. Problem 2aFor every level Kevin completes  To solve this, lets setin his favorite up an expression togame, he earns 800 points. Kev show how manyin already has 450points in thegame and wants to end up with points Kevin willat least 3390 points have after each level.before he goes to bed. What isthe minimum number ofcomplete levelsthat Kevin needs to complete toreach his goal?
25. 25. Problem 2aFor every level Kevin completes Number of pointsin his favoritegame, he earns 800 points. Kev =already has 450 points in the Levels completedgame and wants to end up with ×at least 3390 pointsbefore he goes to bed. What is Points per levelthe minimum number of +complete levelsthat Kevin needs to complete to Starting pointsreach his goal?
26. 26. Problem 2aFor every level Kevin completes Since Kevin wants toin his favorite have atgame, he earns 800 points. Kev least 3390 pointsalready has 450 points in thegame and wants to end up with before going to bed, weat least 3390 points can set up anbefore he goes to bed. What is inequality.the minimum number ofcomplete levelsthat Kevin needs to complete toreach his goal?
27. 27. Problem 2aFor every level Kevin completes  Number ofin his favorite points ≥3390game, he earns 800 points. Kevalready has 450 points in the  Levelsgame and wants to end up with completed × Pointsat least 3390 points per level + Startingbefore he goes to bed. What is points ≥3390the minimum number ofcomplete levels that Kevin needs to complete toreach his goal?
28. 28. statistics  http://bag.sh/26ku+