
Example: The sum of three consecutive integers is equal to the greatest of these integers plus 15. What are the integers? Solution: Translate the statement to a math equation, and then solve the equation. Let the first consecutive integer be 'x'. The second consecutive integer follows right after the first, so it must be one greater. Therefore, it is x+1. The third consecutive integer is one greater than the second, so it is x + 1 + 1 = x + 2 The sum of three consecutive integers is x + x + 1 + x + 2 = 3x + 3 The question states that the sum of three consecutive integers is equal to the greatest of integers plus 15, i.e., (x+2)+15 3x+3 = x+2+15 3x+3 = x+17 3x+33 = x+173 3x = x+14 3xx = x+14x 2x = 14 x = 7 Therefore, the integers x, x+1, x+2 are 7, 8, and 9. Example: There are three consecutive even integers. Half the sum of the second and third numbers is 35. What are the integers? Let the three consecutive even integers x, x+2 and x+4 sum of three consecutive even integers = x+x+2+x+4 sum of the second and third numbers is 35 implies (x+2+x+4)/2=35 (2x + 6)/2 = 35 2x + 6 = 70 2x = 706 2x = 64 x = 32 x + 2 = 34 x + 4 = 36 Example: The sum of two consecutive integers is 23. What is the second number? Let the first consecutive integer be a. The second consecutive integer is one more than the first. That is b = a+1. The sum of two consecutive integers is 23 a + b = 23 substituting b = a+1 a + (a+1) = 23 a + a + 1 = 23 2a + 1 = 23 2a = 22 a = 11 Therefore b = a + 1 = 12 Example: What are two consecutive integers, such that seven times the larger minus three times the smaller is 95? Let the first consecutive integer be a. The second consecutive integer is one more than the first. That is b = a+1. seven times the larger minus three times the smaller is 95 b = a + 1 7b  3a = 51 7(a + 1)  3a = 51 7a + 7  3a = 51 4a + 7 = 51 4a = 51  7 4a = 44 a = 11 b = a + 1 = 11 +1 = 12 Example: What is the average of the first 45 integers? Solution: The average of a set of consecutive integers is same as the average of the first and last integers (1 + 45) / 2 = 46/2 = 23 Directions: Solve the unknown for the following word problems. 