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Steps to Solving Word Problems 1. 2. 3. 4. 5. 6. 7. Use a variable to represent the unknown quantity Express any other unknown quantities in terms of this variable, if possible. Write an equation, and solve it. State the answer to the problem. Check your answer by substituting in the problem. If Age question, use a chart to organize information. If a distance, time, speed question, use a chart to organize information. The sum of two consecutive odd numbers is 32. What are the numbers Let x represent the one number. Let (x + 2 ) represent the other number. Equation: x + (x + 2) = 32 x + (x + 2) = 32 Things to Remember: Use a variable to represent the unknown quantity 2x +2 = 32 Express any other unknown quantities in terms of this variable, if possible. 2x + 2 - 2 = 32 - 2 Write an equation, and solve it. 2x = 30 2x = 30 2 2 State the answer to the problem. x = 15 x + 2 = 17 Check your answer by substituting in the problem. The sum of two consecutive even numbers is 34. What are the numbers Things to Remember: Equation: Use a variable to represent the unknown quantity Express any other unknown quantities in terms of this variable, if possible. Write an equation, and solve it. State the answer to the problem. Check your answer by substituting in the problem. The sum of two consecutive even numbers is 34. What are the numbers Let x represent the one number. Let (x + 2 ) represent the other number. Equation: x + (x + 2) = 34 x + (x + 2) = 34 Things to Remember: Use a variable to represent the unknown quantity 2x +2 = 34 Express any other unknown quantities in terms of this variable, if possible. 2x + 2 - 2 = 34 - 2 Write an equation, and solve it. 2x = 32 2x = 32 2 2 State the answer to the problem. x = 16 x + 2 = 18 Check your answer by substituting in the problem. You have 3 less nickels than dimes. If you have $1.05, how many dimes do you have? (Money Question) Let x represent the number of dimes. Let (x - 3) represent the number of nickels. Equation: 0.1x + 0.05(x - 3) = 1.05 0.1x + 0.05x - 0.15 = 1.05 Things to Remember: Use a variable to represent the unknown quantity 0.15x - 0.15 = 1.05 Express any other unknown quantities in terms of this variable, if possible. 0.15x - 0.15 + 0.15 = 1.05 + 0.15 Write an equation, and solve it. 0.15x = 1.20 0.15x = 1.20 0.15 0.15 State the answer to the problem. x=8 Check your answer by substituting in the problem. (Money Question) You have 6 less nickels than quarters. If you have $2.40, how many quarters do you have? Things to Remember: Equation: Use a variable to represent the unknown quantity Express any other unknown quantities in terms of this variable, if possible. Write an equation, and solve it. State the answer to the problem. Check your answer by substituting in the problem. You have 6 less nickels than quarters. If you have $2.40, how many quarters do you have? (Money Question) Let x represent the number of quarters. Let (x - 6) represent the number of nickels. Equation: 0.25x + 0.05(x - 6) = 2.40 0.25x + 0.05x - 0.3 = 2.40 Things to Remember: Use a variable to represent the unknown quantity 0.3x - 0.3 = 2.40 Express any other unknown quantities in terms of this variable, if possible. 0.3x - 0.3 + 0.3 = 2.40 + 0.3 Write an equation, and solve it. 0.3x = 2.70 0.3x = 2.70 0.3 0.3 State the answer to the problem. x=9 Check your answer by substituting in the problem. (Distance, speed, NO TIME) Jim ran 1.3 times faster than Bill during the 100 m dash. The difference in their speed was 18 m / h. Find the speed of each racer. Let x represent the speed of Bill. Let 1.3x represent the speed of Jim. Equation: 1.3x - x = 18 1.3x - x = 18 Things to Remember: Use a variable to represent the unknown quantity Express any other unknown quantities in terms of this variable, if possible. 0.3x = 18 Write an equation, and solve it. 0.3x = 18 0.3 0.3 State the answer to the problem. x = 60 m / h 1.3x = 78 m / h Check your answer by substituting in the problem. Jill biked 2.1 times faster than Amy during a race. The difference in their speed was (Distance, speed, NO TIME) 22 km / h. Find the speed of each racer. Things to Remember: Equation: Use a variable to represent the unknown quantity Express any other unknown quantities in terms of this variable, if possible. Write an equation, and solve it. State the answer to the problem. Check your answer by substituting in the problem. Jill biked 2.1 times faster than Amy during a race. The difference in their speed was (Distance, speed, NO TIME) 22 km / h. Find the speed of each racer. Let x represent the speed of Amy. Let 2.1x represent the speed of Jill. Equation: 2.1x - x = 22 2.1x - x = 22 Things to Remember: Use a variable to represent the unknown quantity Express any other unknown quantities in terms of this variable, if possible. 1.1x = 22 Write an equation, and solve it. 1.1x = 22 1.1 1.1 State the answer to the problem. x = 20 km / h 2.1x = 42 km/ h Check your answer by substituting in the problem. Class Work Pass in Lesson 3(3) - Equation Word Problem Assignment. Copy down examples Complete Lesson 4 (Page 169 - #13-17)