1 / 66

Grade 10 Academic Math Chapter 1 – Linear Systems

Grade 10 Academic Math Chapter 1 – Linear Systems. Modelling Word Problems Days 4 through Days 9. Day 4 Agenda. Warm-up Types of Modelling Problems Mixture Problems Relative Value Problems Practice. Learning Goal. By the end of the lesson…

mitch
Download Presentation

Grade 10 Academic Math Chapter 1 – Linear Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Grade 10 Academic Math Chapter 1 – Linear Systems Modelling Word Problems Days 4 through Days 9

  2. Day 4 Agenda • Warm-up • Types of Modelling Problems • Mixture Problems • Relative Value Problems • Practice

  3. Learning Goal By the end of the lesson… … students will be able to read and interpret a mixture or relative value word problems and create a pair of linear relation equations, resulting in a linear system

  4. Curriculum Expectations • Solve problems that arise from realistic situations described in words… by choosing an appropriate algebraic… method • Ontario Catholic School Graduate Expectations: The graduate is expected to be… a self-directed life long learner who CGE4f applies effective… problem solving… skills

  5. Mathematical Process Expectations • Connecting – make connections among mathematical concepts and procedures; and relate mathematical ideas to situations or phenomena drawn from other contexts

  6. Modelling Types • 1. Break-Even Problems • 2. Mixture Problems • 3. Relative Value Problems • 4. Rate Problems

  7. Mixture Problems • 2 things come together to give a total number or amount • 2 things come together to form a total cost, weight, points, etc. • Equations are usually in form Ax + By = C

  8. Mixture Problems • Ex. 1 Henry sharpens figures skates for $3 a pair and hockey skates for $2.50 per pair. If he earns $240 and sharpens 94 pairs of skates, how many pairs of each type of skate does he sharpen?

  9. Example 1 Mixture (Cont’d)

  10. Mixture Problems Let x represent # of figure skates Let y represent # of hockey skates x + y = 94 (# of skates eq’n) 3x + 2.5y = 240 (earnings eq’n)

  11. Mixture Problems • Ex. 2 Joe has 38 loonies and toonies totalling $55. How many of each type of coin does he have?

  12. Example 2 Mixture (Cont’d)

  13. Mixture Problems Let l represent # of loonies Let t represent # of toonies l + t = 38 (# of coins equation) l + 2t = 55 (value equation)

  14. Mixture Problems • Ex. 3 (p.44, #11e) • Benoit invested some money at 8% and some at 10%. He earned a total of $235 in interest.

  15. Example 3 Mixture (Cont’d)

  16. Mixture Problems Let x represent Amount of $ invested at 8% Let y represent Amount of $ invested at 10% 0.08x + 0.1y = 235 (interest equation) Note: In order to do a $ invested eq’n, we need the amount invested

  17. Mixture Problems • Ex. 4, p.51, #4c • The total value of nickels and dimes is 75¢

  18. Example 4 Mixture (Cont’d)

  19. Mixture Problems Let n represent # of nickels Let d represent # of dimes 0.05n + 0.10d = 0.75 (value equation) Note: In order to do a # of coins eq’n, we need to know the # coins

  20. Relative Value Problems • Usually 2 unknown numbers, ages, etc. • No set form to the equations • Must follow the directional words such as more than, less, times, is, twice, sum, difference, etc.

  21. Relative Value Problems • Ex. 1, p.51, #7 • The sum of two numbers is 72. Their difference is 48. Find the numbers.

  22. Example 1 Relative Value (Cont’d)

  23. Relative Value Problems Let x represent the first number Let y represent the other number x + y = 72 (sum equation) x – y = 48 (difference equation)

  24. Relative Value Problems • Ex. 2, p.51, #8) • A number is four times another number. Six times the smaller number plus half of the larger number equals 212. Find the numbers.

  25. Example 2 Relative Value (Cont’d)

  26. Relative Value Problems Let x represent the first number Let y represent the other number x = 4y (multiplication eq’n) 0.5x + 6y = 212 (difference equation)

  27. Relative Value Problems • Ex. 3, p.24, #7 • At the December concert, 209 tickets were sold. There were 23 more student tickets sold than twice the number of adult tickets. How many of each were sold?

  28. Example 3 Relative Value (Cont’d)

  29. Relative Value Problems Let x represent # of student tickets Let y represent # of adult tickets x - 23 = 2y (relative # of tickets) x + y = 209 (# of tickets)

  30. Relative Value Problems • Ex. 4, p.24, #8 • A rectangle with a perimeter of 54cm is 3m longer than it is wide. What are its length and width?

  31. Relative Value Problems Let l represent width of the rect. Let w represent length of the rect. 2x + 2y = 54 (perimeter eq’n) l – 3 = w (relative length to width eq’n)

  32. Humour Break

  33. Break-Even Problems • Usually look for the point at which two things cost the same • Can refer to the point at which cost and number of things are equal • Equations usually take the form of y = mx + b

  34. Break-Even Problems • Ex. 1. Barney’s Banquet Hall charges $500 to rent the room, plus $15 for each meal and Patrick’s Party Palace charges $400 for the hall plus $18 for each meal. When will both places cost the same amount?

  35. Example 1 Break-Even (Cont’d)

  36. Break-Even Problems Let x represent # meals Let y represent the cost y = 15x + 500 (Barney’s BH) y = 18x + 400 (Patrick’s PP)

  37. Break-Even Problems • Ex. 2. The Millennium Wheelchair Co. has just started its business. It costs them $125 to make each wheelchair plus $15,000 in start-up costs. They plan to sell the chairs for $500 each. How many chairs do they have to sell in order to break even?

  38. Example 2 Break-Even (Cont’d)

  39. Break-Even Problems Let x represent # of wheelchairs Let y represent cost or revenue y = 125x + 15000 (Cost eq’n) y = 500x (Revenue eq’n)

  40. Break-Even Problems • Ex. 3. p.44, #11c • It costs $135 to rent the car, based on $25 per day, plus $0.15/km

  41. Example 3 Break-Even (Cont’d)

  42. Break-Even Problems Let x represent # of days Let y represent # of km driven 25x + 0.15y = 135 (Cost eq’n) Note: This is not a usual example. Usually if you are dealing with car rental, you have an eq’n like y = 0.15x + 25

  43. Humour Break

  44. Rate (Speed Distance Time) Problems (Copy) • Usually looking for time, speed or distance • Distance = Speed x Time (from science – can be rearranged for speed and time also) • Easiest to use a chart to help develop the equations

  45. Rate (Speed Distance Time) Problems • But first, we have the Distance = Speed x Time (equation) Or... D = S x T

  46. Rate (Speed Distance Time) Problems • We can also rearrange this eq’n to solve for speed... Speed = Distance ------------ Time Or...

  47. Rate (Speed Distance Time) Problems • We can also rearrange this eq’n to solve for Time... Time = Distance ------------ Speed

  48. Rate (Speed Distance Time) Problems • Ex. 1 Fred travelled 95 km by car and train. The car averaged 60 km/h and the train averaged 90 km/hr. If the trip took 1.5 hours, how long did he travel by car? • Let’s use a speed distance time chart to organize our information...

  49. Example 1 Rate (Cont’d)

  50. Rate (Speed Distance Time) Problems Let x represent the time in the car Let y represent the time on the train

More Related