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Q: What are the consecutive integers whose sum is 51?

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16,17,18

The integers are 16, 17 and 18.

They are: 49+50+51 = 150

The integers are 16, 17 and 18.

15,17,19

51 / 3 = 1716+17+18 = 51

No possible solution.The sum of any two odd integers is an even integer.

Divide the sum of the three consecutive odd integers by 3: 51 / 3 = 17. The smallest of these integers will be two less than 17 and the largest will be two more than 17, so the three consecutive odd integers will be 15, 17, and 19.

16, 17, 18 Yes.

The only proper factor of 51 that is less than 1/3 of 51 is 3. Divide the sum of three consecutive odd integers by 3: 51/3 = 17. The smallest of these integers will be two less than 17 and the largest will be two more than 17, so the three consecutive odd integers having a sum of 51 are 15, 17, and 19.

Divide the sum of the three consecutive odd integers by 3: 159/3 = 53. The smallest of these integers will be two less than 53 and the largest will be two more than 53, so the three consecutive odd integers will be 51, 53, and 55.

They are: -15-17-19 = -51

25 and 26

The integers are 51, 53, 55 and 57.

50, 51, 52

49, 51

51

50 + 51 + 52 = 153

Divide the sum of the three consecutive odd integers by 3: 183/3 = 61. The smallest of these integers will be two less than 61 and the largest will be two more than 61, so the three consecutive odd integers will be 59, 61, 63.

The numbers are 51, 53, 55 and 57.

Divide the sum of the three consecutive odd integers by 3: -147 /3 = -49. The smallest of these integers will be two less than -49 and the largest will be two more than -49, so the three consecutive odd integers will be -47, -49, and -51.

There are no such answers. The sum of even numbers is even. The sum of odd numbers could be even, but the sum of three consecutive odd numbers is always odd. One could swap the questions to get potentially answerable questions: Sum of 3 consecutive EVEN integers = 150 48 + 50 + 52 = 150 unfortunately, we can already see that if we were to make these odd integers (add 1 to each), we would get 153, not 151. Sum of 3 consecutive ODD integers = 151 49 + 51 + 53 = 153 47 + 49 + 51 = 147 We can see that, whenever we slide our three consecutive integers up one, we raise the value of the sum up 3, and if we jump from odd to odd, or even to even, we raise each integer by 2, so we raise the sum by 6.

The largest possible values for the integers are 47, 49, and 51.

The numbers are 51, 52 and 53.

X + (X + 1) + (X + 2) = 156 3X + 3 = 156 3X = 153 X = 51 51 + 52 + 53 = 156 156 = 156 51, 52, 53 ------------------are your three consecutive integers