## anonymous 4 years ago The sum of three consecutive integers is 72. Find the integers.

1. anonymous

23+24+25=72

2. Mertsj

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

3. anonymous

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 ;)

4. anonymous

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..