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Word Problems
The document provides an overview of solving word problems, explaining the process as reading the problem, representing unknowns with variables, relating the unknowns to given values, writing an equation, solving the equation, and proving the answer. It also defines odd, even, and consecutive numbers and provides examples of representing and solving word problems involving these types of numbers.
Word Problems
- 2. What did youobserve and notice on the video?
- 3.
- 4. What is aword problem?
- 5. Word Problems - isthe translation of story into an equation
- 6. What is thesimilarity between solving one’s problem and solving word problems?
- 7. Process on Solving WordProblems
- 8. The 3 “R’s”and the “ESP” of solving word problems Read the problem thoroughly. Represent the unknown by means of a variable . Relate the unknow to each other and the values given in the problem. Equate from an equation using the facts in the problem. Solve the equation. Prove the answer.
- 9. Solving Word Problems involvingodd, even and consecutive numbers
- 10. • Odd numbers -are whole numbers not divisible by 2. ex: 21, 19, 17, 15 • Even numbers - are whole numbers divisible by 2. ex: 22, 86, 30, 54 • Consecutive numbers - following without interruption ex: 1, 2, 3, 4
- 11. • Consecutve oddnumbers - are odd numbers in uninterrupted order ex: 3, 5, 7, 9 • Consecutive even numbers - are even numbers in uninterrupted order ex: 2, 4, 6, 8
- 12. Examples: Consecutive Numbers Representat ion Consecutive Numbers Representat ion Consecutive Numbers Representat ion 7 8 9 10 11 x X + 1 X+ 2 X + 3 X + 4 72 74 76 78 80 Y Y + 2 Y + 4 Y + 6 Y + 8 101 103 105 107 109 Z Z + 2 Z+ 4 Z + 6 Z + 8
- 13. Examples: 1. The sumof three consecutive numbers is 90. find the numbers. Solution: Let x = the first number then x + 1 = the consecutive next number and x + 2 = the third consecutive number Their sum is 90: x + (x + 1) + (x + 2) = 90
- 14. Examples: Manipulating the equation,we have x + (x + 1) + (x + 2) = 90 x + x + 1 + x + 2 = 90 3x + 3 = 90 3x = 87 x = 29 1st number x + 1 = 30 2nd consecutive number x + 2 = 31 3rd consecutive number Answer: the consecutive numbers are 29, 30, and 31 Proof : 29 + 30 + 31 = 90
- 15. Examples: 2. Find threeconsecutive even numbers whose sum is 108. Solution: Let x = the first even number then x + 2 = the second even number and x + 4 = the third consecutive even number Their sum is 108: x + (x + 2) + (x + 4) =108 x + x + 2 + x + 4 = 108 3x + 6 = 108 3x = 102 x = 34 1st number x + 2 = 36 2nd consecutive number x + 4 = 383rd consecutive number
- 16. Examples: 3. Find threeconsecutive odd integer whose sum is 57. Solution: Let x = the first odd number then x + 2 = the second odd number and x + 4 = the third consecutive odd number Their sum is 57: x + (x + 2) + (x + 4) =57 x + x + 2 + x + 4 = 57 3x + 6 =57 3x =51 x = 17 1st number x + 2 = 19 2nd consecutive number x + 4 = 21 3rd consecutive number
- 17. Solve the following: 1.Find two consecutive numbers such that twice the larger is 40 less than three times the smaller. 2. Find two consecutive odd numbers such that the difference of their square is 160. 3. Find three consecutive numbers so that twice the first added 5 times the second exceeds three times the third by 51.
- 18. Is there anyquestion?