Name: ___________________________________ Date: _______________________________ 3.5 Modelling With Algebra (part 2) Minds on: 1. Lake Ontario is 77km shorter than Lake Erie. The lengths of the two lakes total 699km. Write an equation to find the length of Lake Ontario. 2. Fred has $10 more than Barney. Together, they have $120. Write an equation to find the amount they have. 3. The area of the triangle is three times the area of a square. The sum of their areas is 230m³. Write an expression to represent their areas. Page 1 of 4 MPM1DY Mr. V VSS Grade 9 Academic Math Lesson learning goals: • • Model a problem using algebra Solve algebraic models using a variety of methods When modelling with algebra, ensure the follow these steps for full marks: 1. 2. 3. 4. 5. write the introductory sentence(s) identifying the variables write the equation simplify the equation solve (if needed) write a concluding sentence 1. The sum of three consecutive odd integers is 57. a) Let x represent the least integer. Write an algebraic expression to represent each of the other integers. b) Write an equation to represent the sum of the integers. c) Find the integers. 2. Three consecutive even integers have a sum of 102. a) Write an algebraic expression to represent each integer. b) Write an equation to represent the sum of the integers. c) Find the integers. Page 2 of 4 MPM1DY Mr. V VSS Grade 9 Academic Math 3. The length of a rectangle is triple its width. The perimeter of the rectangle is 40 cm. What are the length and width? 4. The sum of two numbers is 42. One number is 8 less than the other. What are the two numbers? 5.The sides of a triangle are 3 consecutive whole numbers in centimetres. The perimeter of the triangle is 48cm. How long is each side? Page 3 of 4 MPM1DY Mr. V VSS Grade 9 Academic Math 6. A large painting costs $75 more than a smaller painting. Together, they cost $725. How much does each cost? 7. A parking meter contains $27.05 in quarters and dimes. There are 146 coins. How many quarters are there? 8. Determine expressions to represent the dimensions of a rectangular prism V = x3 + 5x2 + 6x when x = 3cm. Page 4 of 4