Presentation on theme: "Grade 10 Academic Math Chapter 1 – Linear Systems Modelling Word Problems Days 4 through Days 9."— Presentation transcript:
Grade 10 Academic Math Chapter 1 – Linear Systems Modelling Word Problems Days 4 through Days 9
Day 4 Agenda 1.Warm-up 2.Types of Modelling Problems 3.Mixture Problems 4.Relative Value Problems 5.Practice
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
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
Mathematical Process Expectations Connecting – make connections among mathematical concepts and procedures; and relate mathematical ideas to situations or phenomena drawn from other contexts
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
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?
Mixture Problems Let x representAmount of $ invested at 8% Let y representAmount 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
Mixture Problems Ex. 4, p.51, #4c The total value of nickels and dimes is 75¢
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
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?
Break-Even Problems Let x represent# meals Let y representthe cost y = 15x + 500 (Barney’s BH) y = 18x + 400 (Patrick’s PP)
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?
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
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
Rate (Speed Distance Time) Problems But first, we have the Distance = Speed x Time (equation) Or... D = S x T
Rate (Speed Distance Time) Problems We can also rearrange this eq’n to solve for speed... Speed = Distance ------------ Time Or...
Rate (Speed Distance Time) Problems We can also rearrange this eq’n to solve for Time... Time = Distance ------------ Speed
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...
Rate (Speed Distance Time) Problems Ex. 2 (text p.137, #6) A traffic helicopter pilot finds that with a tailwind, her 120km trip away from the airport takes 30 minutes. On her return trip to the airport, into the wind, she finds that her trip is 10 minutes longer. What is the speed of the helicopter? What is the speed of the wind?