Question 221142: Show the impossible for three consecutive integers to have a sum that is 200 more than the smallest integer. Answer by drj(1380) (Show Source):
You can put this solution on YOUR website! Show the impossible for three consecutive integers to have a sum that is 200 more than the smallest integer.
Step 1. Let n be the integer
Step 2. Let n+1 and n+2 be the next two consecutive integer.
Step 3. Then n+n+1+n+2=3n+3=3(n+1) be the sum of the three consecutive integers.
Step 4. Let 200+n be 200 more than the smallest integer.
Step 5. Equate steps 3 and 4.
Subtract n+3 from both sides of the equation
Divide by 2 to both sides of the equation
This statement does not provide a whole integer n since 197 is odd and not divisible by 2.
Step 6. Note that 197/2 is not a whole number so it's impossible for three consecutive integers to have a sum that is 200 more than the smallest integer.
I hope the above steps and explanation were helpful.
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