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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation2.3 Word Problems - Basic Operations With Variables - 3

 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+3-3 = x+17-3 3x = x+14 3x-x = x+14-x 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 = 70-6 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.
 Q 1: The sum of three consecutive integers is 30. What are the integers?7,8,99,10,118,9,10 Q 2: The average of the eleven consecutive odd integers is 17. What is the first of these integers? Hint: Eleven consecutive odd integers are x, x+2, x+4, x+6, x+8, x+10, x+12, x+14, x+16, x+18, x+20. Their average is 11597 Q 3: The average of a set of consecutive integers is 45. The last integer is twice the first integer. What is the last integer? (Hint: The average of a set of consecutive integers is same as the average of the first and last integers!)last integer = 30last integer = 40last integer = 60last integer = 80 Q 4: The sum of four consecutive multiples of 5 is equal to the product of the first integer and 5. What is the first integer? (Hint: Let the first integer be x, then first four multiples of 5 are 5,10,15,20. Their sum equals to product of first integer and 5 can be written as 5+10+15+20 = 5x. Solve for x) 109158 Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!