Consecutive Even or Odd Integer Problems
| Step 1 | Call the first integer x. |
| Step 2 | Make a table that has a variable expression for every unknown integer that the problem requires. (Keep in mind that both consecutive even and odd integers are two apart.) |
| Step 3 | Write an equation that reflects the information in the problem. (Look for the is.) |
| Step 4 | Solve the equation. |
| Step 5 | Answer the question. |
Directions: Please answer the following question.
The sum of four consecutive odd integers is 464. What is the product of the second and third integers?
| Step 1 | Let x = 1ST integer | ||||||||
| Step 2 |
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| Step 3 | x+(x+2)+(x+4)+(x+6)=464 | ||||||||
| Step 4 | 4x+12=464 4x=452 x=113 |
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| Step 5 | The second and third integers
are 115 & 117 There product is 115*117=13455 |
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The sum of 3 consecutive even integers is ten more than three times the third integer. What is the product of the first and second integer?
| Step 1 | Let x = 1ST integer | ||||||
| Step 2 |
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| Step 3 | x+(x+2)+(x+4)=2(x+4)+10 | ||||||
| Step 4 | 3x+6=2x+8+10 3x+6=2x+18 x+6=18 x=12 |
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| Step 5 | The first and second integers
are 12 & 14 There product is 12*14=168 |
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Directions: Please answer the following questions.
1. The sum of three consecutive odd integers is 63. What is the third integer?
2. The sum of four consecutive even integers is 316. What are the four integers?
3. The sum of four consecutive even integers is 3956. What is the third integer?
4. The sum of three consecutive even integers is 20 less than four times the first integer. What are the integers?
5. The sum of three
consecutive odd integers is 21 more than twice the third
integer. What are the integers?
Directions: Please write 1-2 paragraphs that thoroughly address the following.
Consider the chart used in example 1 above and compare it to the chart used in example 2. If the problem in example 1 involves consecutive odd integers and the problem in example 2 involves even integers, why are the charts so similar?