anonymous
  • anonymous
The sum of three consecutive integers is 72. Find the integers.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
23+24+25=72
Mertsj
  • 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
anonymous
  • 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 ;)

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anonymous
  • 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..

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