- Answered by a verified Math Tutor or Teacher. 3a + 6 = 48. We could call the numbers x,x+2andx+4 , but there is no guarantee that x is even. Therefore, three consecutive integers that add up to 96 are 31, 32, and 33. 3a+0=54. Thus, 3x+6=108. The smallest number among these are 14 Explanation: Three consecutive even integers can be represented by x, x+2, x+4. The answer will always be divisible by 6 because in . SOLUTION: Find three consecutive even numbers whose sum is ... The key word here is "Average". The sum of three consecutive even numbers is 54 . Find the ... Therefore, the sum of three consecutive odd integers is Solution: Given, The sum of three consecutive even numbers is 84. Solving for x yields x=34. Therefore, we can express the numbers as follows: * let X be the first number in the sequence. The sum of three consecutive odd numbers and three consecutive even numbers together is 231.Also, the smallest Odd number is 11 less than the Smallest even number. The sum of three consecutive even numbers is 54. Correct! However, an even number can be divided by 2, so any nu. Thus, 3x+6=108. Let us find their product; 11 × 13 = 143 However, the question asks for the largest number, which is x+4 or 38. You can try a bit of logic. Medium Solution Verified by Toppr Sum of three consecutive integers can be written as. Example: The product of two consecutive odd numbers is 143. How do you find the numbers? Answer (1 of 9): For those who find algebra a bit difficult. A problem may ask about consecutive even numbers—2, 4, 6, 8, 10—or consecutive odd numbers—13, 15, 17—where you take one even number and then the very next even number after that or one odd number . 2n + 2n + 2 + 2n + 4 = 84 6n + 6 = 84 6n = 84 - 6 6n = 78 n = 78/6 n . differ by 2. Algebra. Easy. a = 18 a−1. You could have also plugged in the answer choices. So, the sum of the consecutive even numbers = 48. What 3 consecutive numbers equal 90? =18−1 = 17 ========Ans 1. a = 18 Ans 2. and a+1. You would then put them into an equation. Let's look at another example: the sum of 5 consecutive even integers is 120. What is the smallest of these numbers? Question: 2) If x is a number, give an expression for the even number that is consecutive to x. In a set of consecutive numbers,the mean and the median are Equal. Combine like terms on the right side. Medium. Medium. If the first number is n, then the second number is n+2 and the third number is n+4. 2. In here, M = 3, S = 258. Let the three consecutive even numbers be x, x +2 and x +4. The answers 6, 24, 60 are all divisible by 6, because each product has an even number and a multiple of 3. Find the numbers. Example 2: The sum of three consecutive even numbers is 24. 3a− 1+1=54. 31 + 32 + 33 = 96 We know our answer is correct because 31 + 32 + 33 equals 96 as displayed above. Three consecutive even integers can be represented by x, x+2, x+4. The sum of three consecutive even numbers is 2 7 6. x + 2 = length of second shelf. Being consecutive and even, we know it is 2. x+(x+2)+(x+4)=54 Simplify this to 3x+6=54, subtract 6 from both sides to get 3x=48, and then divide both sides of the equation by 3 to get x=16. The Sum Of Three Consecutive Even Numbers Is 48 What Is The Smallest Of These Numbers The sum of three consecutive even numbers is 48. The sum of three positive number is 30. Consecutive numbers are numbers that follow each other in order. Menu. 2) If x is a number, give an expression for the even number that is consecutive to x. Assign variables: Let x = length of first shelf. Example 4. x + 4 = length of third shelf. We should choose the numbers whose product is nearly 143. Use this formula to calculate: First(e) = 234 / 3 - 3 + 1 = 78 - 3 + 1 = 76 It is exactly the same as the result of the above non-formula calculation. We should choose the numbers whose product is nearly 143. The numbers are all even, and they are consecutive to each other. x + 6 = length of fourth shelf. 3 × 12 = 36. What three consecutive integers have a sum of 180? Email: donsevcik@gmail.com Tel: 800-234-2933; Add the terms and equate it with the total, 48 . The sum of three consecutive even numbers is 2 7 6. 3a = 48 - 6 . Let us assume the three consecutive even numbers of series to be x,x+2 and x+4. or. x = 96 3 = 32. - Get the answer to this question and access a vast question bank that is tailored for students. View solution > View more. Sum of Three Consecutive Integers Calculator. 2 x 3 x 4= 24. Consecutive odd numbers near 12 are 11 and 13. Step 1: Being consecutive even numbers we need to add 2 to the previous number. Using the formula, the first . But, 12 is an even number. View solution > Find three consecutive numbers whose sum is 1 0 8. Therefore, the three consecutive even integers are 58,60,62 . To get the Average divide the sum (144) by the quantity of numbers that were added (3), then disperse the average (144/3=48) among the quantities, in this case you take 2 from. Add the terms and equate it with the total, 48 . A) 82: B) 83: C) 74: D) None of these : Correct Answer: =18+1=19 ========Ans 3. 3x = 102 −6 = 96 and. The formula for consecutive even numbers are 2n, 2n + 2, 2n + 4. What are the numbers? Example 1: Find the two consecutive even numbers whose sum is 66. What is the smallest of these numbers? 2 Answers Jarni Renz Jan 9, 2016 The smallest number is #14# Explanation: Let: x= the 1st con.even number x+2=the 2nd con.even number x+4=the 3rd con.even number. Was this answer helpful? Given : Average of 3 consecutive even numbers - 18 Find : Largest among three consecutive even numbers. Let us see how to find the three consecutive even numbers when the sum is given. So, we can use 2 * N + 1 to represent the first integer, then the second and third odd integers are 2 * N + 3 and 2 * N + 5. Subtract from both sides. Explanation: Suppose the first number of all three consecutive numbers is "a". Start Here; Games; Upgrade to Math Mastery. The answer came out, the sum of 3 consecutive even integers is 258, these three even integers are 84, 86 and 88. However, the question asks for the largest number, which is x+4 or 38. The sum is 3x+6, which is equal to 108. Just like the investigation on sum of consecutive numbers we can start by using three consecutive numbers and multiplying them. Select the numbers so that the product of all three is as large as possilbe. or. Find the numbers. We know that 12 × 12 = 144. Algebraically, they follow the pattern , , , etc So if "The sum of three consecutive even numbers is 150", then the equation is Combine like terms on the left side. Replace them in the formula to calculate the first even integer. Answer (1 of 9): (n-2)+n+(n+2)=1524 \implies 3n=1524 \implies \dfrac{3n}{3}=\dfrac{1524}{3} n-2=\boxed{506} n=\boxed{508} n+2=\boxed{510} x + 4 = length of third shelf. The formula to find the three consecutive numbers is n, n + 1, n + 2. 3a=54. First(e) = 258 / 3 - (3 - 1) / 2 = 86 - 2 / 2 = 86 - 1 = 85 3 x 4 x 5 = 60. x + x + 2 + x + 4 = 102 or. Similar to even numbers, odd numbers are integers that are not divisible by 2. The numbers are all even, and they are consecutive to each other. Math. Step 2: Convert 3 feet to inches. The sum is 3x+6, which is equal to 108. Therefore, we can express the numbers as follows: * let X be the first number in the sequence. Assign variables: Let x = length of first shelf. The first plus twice the second plus three times the third add up to 60. To get a good grasp of the procedure, let's begin by solving a simple problem. This leads to 3n + 6 = 24, and n = 6. The mathematical representation will be : * let Y be the second number in the sequence. Easy. Solution : Let the three consecutive even numbers be x, x+2 and x+4.The sum of these three consecutive even numbers will be : 3x+6. - Get the answer to this question and access a vast question bank that is tailored for students. Divide both sides by to isolate . Find three consecutive even numbers whose sum is 234. What is the sum of the largest odd number and the largest even number ? Formula method Solving for x yields x=34. N + (N + 2) = Total For 2 consecutive even integers N + (N + 2) + (N + 4) = Total For 3 consecutive even integers N + (N + 2) + (N + 4) + (N + 6) = Total For 4 consecutive even integers And so on. Solution: Just like the investigation on sum of consecutive numbers we can start by using three consecutive numbers and multiplying them. Three Consecutive . The sum is 3x+6, which is equal to 108. How do you find the sum of three consecutive integers? What is the smallest of these numbers? Find three consecutive even numbers whose sum is 234. 16 would be your lowest integer, so the next two would be 18 and 20. For geniusy_2006: Three consecutive even integers are such that the square of the third is 100 more than the square of the second. Math. View solution > Find three consecutive numbers whose sum is 1 0 8. The sum of three consecutive even numbers is 84. Consecutive Even Integers: even numbers that are exactly 2 apart (for instance, 14 and 16 are consecutive even integers). 3x+ 6 = 48. 16 would be your lowest integer, so the next two would be 18 and 20. x + 6 = length of fourth shelf. The second consecutive even integer is 2 units more than the first. 0 0 48=x+x+2+x+4. Consecutive Even Integers: even numbers that are exactly 2 apart (for instance, 14 and 16 are consecutive even integers). (a−1)+a+(a+1)=54. Hence. As always, check to make sure that their sum is indeed -78. Thus, 3x+6=108. 3X + 3 = 96 3X + 3 - 3 = 96 - 3 3X = 93 3X/3 = 93/3 X = 31 Which means that the first number is 31, the second number is 31 + 1 and the third number is 31 + 2. x + 2 = length of second shelf. 2 Answers Jarni Renz Jan 9, 2016 The smallest number is #14# Explanation: Let: x= the 1st con.even number x+2=the 2nd con.even number x+4=the 3rd con.even number. 3x +6 = 102 or. It is given that sum of all these three consecutive numbers is 48. Answer (1 of 6): So, we have three numbers. or. Step 1: Being consecutive even numbers we need to add 2 to the previous number. Therefore, three consecutive integers that add up to 120 are 39, 40, and 41. x = 14. View solution > View more. More From Chapter. N + (N + 2) = Total For 2 consecutive even integers N + (N + 2) + (N + 4) = Total For 3 consecutive even integers N + (N + 2) + (N + 4) + (N + 6) = Total For 4 consecutive even integers And so on. Find the numbers. So our three consecutive even integers are: {-28}, {-26}, and {-24}. 3) Write an expression for the sum of three consecutive even numbers and simplify it. The sum of three consecutive even numbers is 48. S stands for sum. 3 × 12 = 36. Given that their sum is 24, hence, we have: n + n+2 + n+4 = 24. Hence, numbers are 32, 34 and 36. So, the sum of the consecutive even numbers = 48 Hence 48=x+x+2+x+4 3x+ 6 = 48 3x = 48-6 3x = 42 The sum of three consecutive even numbers is 48. Please make sure to answer what the question asks for! You could have also plugged in the answer choices. This is the most common method, let's look at the second method, which is my favorite method. Examples of Solving the Sum of Consecutive Even Integers . Math Step 3: Sum of the 4 shelves is 36. Sum of Three Consecutive Integers Video. Solution: Consecutive even numbers have a difference of 2 between them. The numbers 3, 6, 9 are not consecutive numbers, but they are consecutive multiples of 3, which means that the numbers are adjacent integers. Thus the three consecutive even numbers are 2, 4, 6. Reduce. Answer (1 of 8): The numbers are 46, 48 and 50. Answer link. As per the question, the average is 18. They have a difference of 1 between every two numbers. M represents the number of consecutive even integers. Find the numbers. Back to the problem we want to solve: find three consecutive even integers whose sum is 258. Step 3: Sum of the 4 shelves is 36. Therefore, the next two numbers will be (a + 2), and (a + 4). N represents an integer.. The above example: the sum of 3 consecutive even numbers is 234 find the numbers? Being consecutive and even, we know it is 2. Let us find their product; 11 × 13 = 143 1 x 2 x 3 = 6 2 x 3 x 4= 24 3 x 4 x 5 = 60 The answers 6, 24, 60 are all divisible by 6, because each product has an even number and a multiple of 3. You would then put them into an equation. View solution > If the sum of three consecutive even numbers is 2 3 4, then the smallest among them is. Because these are consecutive even numbers, then your values would be x, x+2, and x+4. Explanation: First define the consecutive even numbers: Even numbers, such as 8, 10, 12 etc. Three consecutive even integers can be represented by x, x+2, x+4. So the three numbers are 14,16 and 18. 3x = 48-6. Consecutive odd numbers near 12 are 11 and 13. x+ (x+2)+ (x+4)=54 Simplify this to 3x+6=54, subtract 6 from both sides to get 3x=48, and then divide both sides of the equation by 3 to get x=16. * let Y be the second number in the sequence. Example: The product of two consecutive odd numbers is 143. Medium. Please make sure to answer what the question asks for! But, 12 is an even number. "consecutive even numbers" are integers such as 2, 4, 6, 8, 10, etc. 3X + 3 - 3 = 120 - 3 3X = 117 3X/3 = 117/3 X = 39 Which means that the first number is 39, the second number is 39 + 1 and the third number is 39 + 2. Then. Answer (1 of 6): So, we have three numbers. Answer the three consecutive integers are 28, 30 and 32. There are 3 consecutive even numbers such that twice the first is 20 more that the second. Let 2k be the first even integer. 39 + 40 + 41 = 120 We know our answer is correct because 39 + 40 + 41 equals 120 as displayed above. or. Sum of Three Consecutive Integers calculator. Translate the math sentence " the sum of three consecutive even integers is -78 " into an equation and solve for k. Let's determine the three consecutive even integers by replacing k with its value, which is -14. View solution > If the sum of three consecutive even numbers is 2 3 4, then the smallest among them is. Step 2: Convert 3 feet to inches. Find four consecutive odd integers in which the sum makes 0. The formula for consecutive even numbers are 2n, 2n + 2, 2n + 4, 2n + 6,… The formula for consecutive odd number are 2n + 1, 2n + 3, 2n + 5, 2n + 7,… How to find Three Consecutive Numbers? Let us assume the three consecutive even numbers of series to be x,x+2 and x+4. We know that 12 × 12 = 144. Sum of three consecutive numbers equals . . a=54/3. What are the numbers? Because these are consecutive even numbers, then your values would be x, x+2, and x+4. Algebra. Hence, a + a + 2 + a + 4 = 48. Medium. Algebra questions and answers. More From Chapter. Verify: 84 + 86 + 88 = 258. 3x = 42. x = 42/3. 1 x 2 x 3 = 6. What are the three numbers? Algebra. Are 3 consecutive even numbers = 48 + a + 4 to 60 3! And even, and 33 11 and 13 solve: find the sum of three numbers! '' > what is consecutive to each other ) If x is a number, give an for!: { -28 }, and they are consecutive numbers is 84 to question. 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