Question

The sum of three consecutive integers is 72. Find the integers.

Answer 1

23+24+25=72

Answer 2

x
x+1
x+2 are the consecutive integers
x+(x+1) +(x+2)=72
3x+3=72
3x=69
x=23
x+1=24
x+2=25

Answer 3

There's a 'bad' or 'fast way of doing it...think about 3x20=60 and 3x30 = 90. We know the integers must be between 20 and 30 then. We need their units to sum to 12, and we can achieve this by looking at 3+4+5 hence the integers are 23, 24, 25. But Mertsj's way is most pleasing ;)

Answer 4

The point being, \[3\times 20 \geq x + (x-1) + (x-2)\] for \[x \leq 20\] and \[3 \times 30 \leq y + (y+1)+(y+2)\] for \[y\geq 30\] so we know our sum must be of three consecutive numbers between 20 and 30, then it's just a case of playing with sums of units to get a 12..