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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation2.13 Word Problems - Basic Operations With Variables - Consecutive Integers

 Consecutive integers are integers that follow one another: Example: 1,2,3........ 34,35,36....... -9,-8, -7,........ Let x represent an integer, x+1 represents the next consecutive integer, x+2 the integer after that and so on...... Consecutive even integers are even integers that follow one another. We have to add 2 to the preceding even integer to get to the next consecutive even integer: Example: 6,8,10........ 342, 344, 346...... -12,-10,-8...... If x represents the first even integer x+2 represents the second even integer x+4 represents the third even integer and so on........ x, x+2, x+4............... Consecutive odd integers are odd integers that follow one another. Just as even integers we have to add 2 to the preceding odd integer to get to the next consecutive odd integer: Example: 5,7,9........ 341, 343, 345...... -11,-9,-7...... If x represents the first odd integer x+2 represents the second odd integer x+4 represents the third odd integer and so on........ x, x+2, x+4............... Example: Find two consecutive integers whose sum is 155. Let x = the first integer Let x + 1 = the second integer the sum of two integers is 155 x + x + 1 = 155 2x + 1 = 155 2x = 154 x = 77 x+1 = 77+1 = 78 Answer: The two consecutive integers whose sum is 155 are 77 and 78. Example: Determine three consecutive integers such that twice the sum of the first and second is 27 more than three times the third. Let x = the first integer Let x+1 = the second integer Let x + 2 = the third integer twice the sum of the first and second is 27 more than three times the third: 2(x + x+1) = 3(x+2)+ 27 2(2x+1) = 3x + 6 + 27 4x + 2 = 3x + 6 + 27 4x - 3x = 6 + 27 - 2 x = 33 - 2 x = 31 x+1 = 32 x+2 = 33 Answer: The three consecutive integers are 31, 32, 33 Example: Find the consecutive positive even integers whose sum is 94. Let x = the first even integer Let x + 2 = second even integer sum of the integers is 94: x + x+2 = 94 2x + 2 = 94 2x = 92 x = 46 x+2 = 48 Example: The sum of two consecutive integers is 25. Find the two numbers. Let n be the first integer Then n + 1 is the second even integer sum of the integers is 25 implies that n + (n + 1) = 25 n + (n + 1) = 25 2n + 1 = 25 2n = 24 n = 12 n + 1 = 13 The two numbers are 12 and 13 Example: The product of two consecutive negative even integers is 24. Find the numbers. Let n be the first integer then n + 2 is the second integer n(n+2) = 24 n2 + 2n = 24 n2 + 2n - 24 = 0 (n+6)(n-4)= 0 n = -6 and n = 4 The solutions are n = -6 and n = 4. Since the number we are looking for is a negative the solution is n = -6 n = -6 n + 2 = -6 + 2 = -4 Therefore the two numbers are -6 and -4 Directions: Solve the following equations with three variables.
 Q 1: If three consecutive integers add up to 225, what are they?66, 67, 6871, 72, 7374, 75, 76 Q 2: If 5m+1 represents the first even integer, what are the next two consecutive even integers?5m+3, 5m+55m+2, 5m+45m+2, 5m+3 Q 3: Find the consecutive even integers whose sum is 132.42,44,4636,38,4024,26,28 Q 4: Find three consecutive integers whose sum is 54.17, 18, 1916,17,1812,13,14 Q 5: Find the consecutive odd integers whose sum is 117.23,25,2727,29,3137, 39. 41 Q 6: Find the three consecutive integers such that three times the largest is 9 less than four times the smallest. (Hint: Let three consecutive integers be x, x+1, x+2. three times the largest is 9 less than four times the smallest: 3(x+2) = 4x-9 x=?, x+1=?, x+2=?11,12,1321,22,2315,16,17 Q 7: What are three consecutive integers such that three times the smallest added to 7 is 13 less than four times the largest? (Hint: Let three consecutive integers be x, x+1, x+2. three times the smallest added to 7 is 13 less than four times the largest: 3x+7 = 4(x+2)-14 then x=?, x+1=?, x+2=?8,9,1015,16,1712,13,14 Q 8: Four consecutive integers add up to 98. Find the integers.23, 24, 25, 2619, 20, 21, 2225, 26, 27, 28 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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