consecutive integers?

Question

help...
find the smallest of three consecutive integers whos sum is less than 86

Answer 1

27, 28, 29 = 84 < 86

Let x be the smallest
Let x + 1 be the next
Let x + 2 be the third

x + (x + 1) + (x + 2) < 86
3x + 3 < 86
3x < 83
x < 27 2/3

Since x must be an integer, the next smaller number is x = 27.

27 + 28 + 29 = 84 which is less than 86

Answer 2

Don't you mean
find the smallest of *the largest* three consecutive integers whos sum is less than 86

Otherwise there is no unique solution. I could pick 1, 2, 3. Their sum is 6, which is less than 86.

Answering the problem as revised:

x + (x + 1) + (x + 2) = 3x +3 < 86
3x < 83
x < 83/3 = 27 2/3

Since x must be an integer, we need to round x down to the next smallest integer. So the smallest number is x = 27.

As a check: 27 + 28 + 29 = 84 < 86.

Answer 3

Ok, so you need to set it up as an inequality:
Let x= Smallest variable
Consecutively the next variable would be x+1, then x+2, so plug it in:
x+x+1+x+2<86
3x+3<86
3x<83
x<83/3
x<27 and 2/3
x<27.6666666...
So, if we were trying to find them, with their sum less than 86, the smallest number would have to be les than 27.66666666666...

Answer 4

oh i had to do that once this year, (im in 8th grade) but i cant remember, sorry :( ill think though