Let's call our three integers "s", "m", and "l", "s" being the smallest and "l" being the largest.
Before looking at the equation, we know:
s + 1 = m
m + 1 = l
So the equation you gave me was:
3m = s + l + 5
The easiest way to do this is the substitution method: Since we know what l equals, and we know what m equals, we can substitute them in the third equation.
Let me show you:
3m = s + l + 5
We can replace l with m + 1, since that's what it equals.
3m = s + (m + 1) + 5
At this point, since we already have 2 m's, it will be easier to substitue something for s.
We can find out what s equals by modifying the equation s + 1 = m.
Taking one away from each side will make the equation s = m - 1
So now we know what s equals, and we can substitute it as well:
3m = (m - 1) + (m + 1) + 5
Going on:
3m = m - 1 + m + 1 + 5
3m = 2m + 5
Now just need to isolate the variable m. The easiest way to do this is by subtracting 2m from each side:
(1)m = 5
m = 5
Now that we know what m equals, we can substitute in the other two original equations:
s + 1 = m
s + 1 = 5
Subtracting one from each side:
s = 4
And the next one:
m + 1 = l
5 + 1 = l
6 = l
We now know our three numbers: 4, 5, & 6.
