Question

Three consecutive integers have a sum of 51. Find the integers.

Answer 1

Answer:

  16, 17, 18

Step-by-step explanation:

The middle of three consecutive integers is their average value. The average of three integers is their sum (51) divided by the number of them (3).

  51/3 = 17 . . . . the middle of the three integers.

The integers are 16, 17, 18.

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Maybe you're thinking an equation is necessary. The reasoning about numbers is sufficient to solve the problem, so no equation is necessary.

This sort of problem is often solved by letting the variable represent the smallest integer. If the variable is x, then the three integers are ...

  x, x+1, x+2

and their sum is ...

  (x) +(x+1) +(x+2) = 51

This gives you a 2-step equation:

  3x +3 = 51

  x+1 = 17 . . . . . divide by 3, because we can

  x = 16 . . . . . . . subtract 1; integers are 16, 17, 18

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Another way to solve this problem is the way we did it in words above. Let the variable represent the middle integer. Then the three integers are ...

  x-1, x, x+1

and their sum is ...

  (x-1) +(x) +(x+1) = 51

This gives you a 1-step equation:

  3x = 51

  x = 17 . . . . . . . . divide by 3; integers are 16, 17, 18